Visco elastic foam or "memory foam" is a very different material and perhaps partly because it has such unusual qualities compared to the many other materials used in mattresses, there is also a lot of misinformation "disguised as fact" about it. It is also subject to many different "formulas" in its manufacturing by different companies which change its qualities ... for better or for worse ... and this too becomes the subject of lots of the hype and misinformation you will hear in the world of marketing and selling mattresses.
What are the basic differences in materials used in a mattress?
There are two basic ways that a material in a mattress reacts to weight and pressure.
1. Viscous materials tend to flow away from pressure like a liquid or honey and tend to distribute and absorb energy
2. Elastic materials tend to store energy under pressure and to different degrees push back against compression
Materials like Water and Air, are viscous. They do have some pushback in a mattress enclosure but this comes from the elasticity and resilience of the enclosure or from other materials in the enclosure that holds them not the air or water itself. Viscous materials can be very hard initially with sudden pressure but feel much softer under more gradual pressure (try leaping onto an airbed or waterbed core). This is because viscous materials take time to "give way" to pressure. When they do give way, they give way in any available direction (out to the sides for example) and spread the pressure out through the layer.
Springs and non memory foams (like "normal" polyurethane and latex) are elastic and will recover quickly and with different amounts of "force" behind them (based on how quickly they spring back) to their original shape or length. Both are also breathable enough that the air just goes in and out with little to no resistance in either direction (compression and recovery) so the response from both of these are mainly because of the material itself not from what encloses them (although this will also have some effect). Of course foam has some resistance to airflow in both in and out directions so airflow plays a small part in its qualities while innersprings are not at all affected by air. Compression of an elastic material works in real time so it would initially feel much softer than a viscous material if you leaped on it but it only gives way in one direction (underneath you) so it will store energy underneath you (and push back) and may feel softer initially but firmer than a viscous material after a matter of some seconds. They have "bounce" in other words and this bounce is called resiliency.
Natural fibers are elastic and resilient to much lesser degrees but not viscous. They are very breathable so the air in them would flow away easily as they compress under pressure but the fibers are not nearly as elastic (stretchable) or resilient (bouncy) as non memory foam or springs and don't "recover" as easily (horsehair is the most resilient of the commonly used fibers and recovers more strongly than wool which recovers more strongly than cotton). These are so breathable that there is very little resistance to air flow under compression (the air inside them moves away really easily) but since most fibers don't have the resiliency to recover with as much force as springs or most foams and are less elastic, they will become more "permanently" compressed to differing degrees over time. They tend to need a resilient support layer underneath them.
Memory foam has a combination of viscosity and elasticity which is why its often called "visco-elastic" and is so different from other materials. It is made in such a way that its ability to recover over time (a period usually measured in seconds) is strong enough (even though it is slower) to "refill" the air but it is not strong enough to be resilient so it absorbs the energy of compression more than returns it with a "springy" feeling. It is less breathable and in the same way that it is more difficult to breathe in or out through a thick fabric, under compression the air both leaves and comes back against more resistance than most other foams. This is part of why it is slower than other materials to compress and return. A bigger reason for this though is that the material itself also changes under pressure and heat from your body or room temperature from a more elastic material into a more viscous material. This change or "melting" also takes time when you lie on it and it also takes time to change back to elasticity and return to its shape when you get up. These two factors are the main reasons that lead to the slower compression and recovery (the memory quality) of memory foam. It also needs a good support layer underneath it.
Materials in a mattress that absorb compression forces and redistribute pressure away from pressure points are great for pressure relief but not usually as good for support. Layers that store energy and push back can also be very good at pressure relief in softer versions but are also better for support. This also depends to some degree on the point elasticity of the material and its ability to form a conforming cradle that mirrors the shape of the body. All viscous materials are good at this. Some elastic and more resilient materials are better at this than than others. The different layers in a mattress are usually designed in such a way that the complete mattress will have both supportive qualities and pressure relieving qualities. The core of the mattress which is the middle and bottom parts (usually innersprings, latex, or higher quality polyfoam) is the part that is primarily responsible for supporting the heavier parts of your body and keeping them from sinking in too far. The comfort layers which is the few inches (usually polyfoam, latex, memory foam, natural wool, horsehair, or synthetic fibres) are responsible for redistributing pressure so you don't get "pressure points" when you sleep. They are also responsible for supporting the inner or more recessed parts of your body (like the small of your back, waist, upper thighs etc) so that gravity doesn't pull them down against the natural position or curvature of your spine. These parts of your body don't usually sink in enough for the deeper support layers to truly support them.
So what does all this mean in mattress terms?
Its unique combination of qualities leads to the advantages of memory foam for some ...
Memory foam's greatest advantage, because of its combination of properties, is generally considered to be its ability to distribute and relieve pressure. This does not mean however that it is dramatically better than the best of other materials as there are other types of foam like latex or high quality polyfoam that in their softer versions through compression alone are very close to memory foam in their ability to distribute pressure to levels below personal detection for most people. Even natural fibers that have broken in and formed a "cradle" to your body can distribute pressure very well and are often used in high quality mattresses. I should also mention here that there is one other material called "buckling gel" that in some cases may even be superior to memory foam or latex in terms of pressure relief but it is newer, not as common, and rather expensive. If a mattress relieves pressure below levels that you personally can detect, then which material is used in the comfort layers to do this is not so relevant except for other reasons such as its ability to support, its breathability, and its durability. In hospital applications (such as the relief of pressure sores) or with highly sensitive people, this slight difference in pressure relief can be more important however in most applications the difference is not as critical or even noticeable and the difference in materials used for pressure relief is more about how they feel and personal preference.
Another advantage of memory foam over a liquid or air is that memory foam requires body heat (in differing degrees with different formulations) to become viscous enough to "flow" so the "unmelted" areas of foam that are further away from your body will be firmer and resist pressure without "flowing away" from that pressure. This means that you are enclosed in a "stable cradle" of material that is "softer" close to you while it remains "firmer" further away from you. This combination of softness and firmness feels very good to people who like to sleep "in" a mattress that also feels "stable". Without this ability and the difference in viscosity and elasticity in different parts of the mattress, you would be sleeping "in" a viscous material which felt more like water or jelly without the feeling of "stable softness" that comes from a good memory foam layer. Other more elastic foams and natural materials to greater or lesser degrees are able to combine a feeling of softness with stability as well but memory foam is the leader here.
The qualities that provide this "stable cradle" effect is also connected to another of memory foam's attractions to some which is its ability to isolate movement between people sleeping on a mattress. Its ability to absorb energy and isolate movement is better than most other materials because of its ability to both absorb energy and respond locally to movement. Latex in a comfort layer is also excellent here because of its ability to "localize" compression better than other materials but it doesn't absorb energy nearly as much. Latex, certain high quality polyfoams, and certain innersprings (like pocket coils) in the support layers also contribute to a mattress' ability to isolate movement and what is under your memory foam is important if this is a desirable part of a mattress' qualities for you.
Memory foam, at least if it is a good quality and higher density memory foam (5 lbs density or above), is also more durable, will keep its qualities, and last longer than many other polyfoams that are typically used in a mattress, especially in the upper comfort layers. It is not unreasonable to expect the best quality memory foams to last 8 - 12 years (depending on its use and the "stresses" it is exposed to). This is not as long however as some very high quality polyfoams, latex foams, better quality innersprings, or natural fibers used in "upper end" mattresses, all of which can last longer without breaking down.
The same combination of qualities which are attractive to some can also be responsible for memory foam's weaknesses for others ...
Because of its low resilience, memory foam is a poor deep support material (the part of your mattress that supports the heavier parts of your body that want to sink in more). This is why it is so important to pay attention to the qualities of the layers underneath the memory foam in a mattress as this is where the deep support (ability to keep your spine aligned) comes from. Treating memory foam as "supportive" as opposed to "pressure relieving" will usually lead to a potential purchaser paying less attention to underlying parts of the mattress and their resilience and other qualities, and possibly choosing a mattress with a poor ability to provide correct alignment for a particular body weight distribution and/or different sleeping positions. Because memory foam can allow you to keep sinking in further over time as it heats up, the underlying parts of the mattress is what will prevent your heavier parts from sinking in so far that your spine is out of alignment.
Some side effects of memory foam's greater sensitivity to heat can also lead to sleeping issues for some people. The deeper in a mattress someone sleeps, the more likely someone is to have issues with "sleeping hot". This of course is a quality of all foams where you "sink in" to some degree but it is compounded by the makeup of memory foams in general which allow a greater degree of sinking in and are typically less breathable (allow for less evaporation) than other foams. Even the newer generation memory foams which are more breathable (and usually a little "quicker") tend to be less so than other foams that are readily available. The greater breathability of other foams which have a more "open" cell structure (like latex or other polyfoams) tend to lessen the heat issues even for those who like to sleep more "in" a mattress using softer "non memory" foams. Natural fibers breathe best of all and tend to be cooler than any foam ... especially memory foam.
This same sensitivity to heat can also lead in some cases to a mattress becoming "too soft" or "too hard" depending on the external temperature in your bedroom, and can change its feel from season to season or from what you experienced in the store depending on environmental conditions. Different types of memory foam can be more or less sensitive to this but it can be more important to control the temperature of your bedroom with some memory foams than it is with others or with other materials.
Another potential issue of memory foams is that they take more time to adjust to different positions. This can be an issue for those who change positions often or are sensitive to the time it takes for the memory foam to conform to their new position as it can create short term "pressure" while it forms a new "cradle". Again different types of memory foams will take shorter or longer to conform to a new position. This "time to compress" or "rebound" that changes with temperature is both part of memory foam's strength for some (creates a "stable cradle") and its weakness for others (doesn't conform to new positions quickly enough or feels too firm). Some people may also be sensitive to a lack of resiliency or "pushback" which allows them to change positions more easily with a little "help" from the mattress and helps to support the lumbar area. This same lack of resiliency or "springiness" is also why it is often rated lower than other materials for the "other activities that take place on a mattress".
Finally there are the "offgassing issues" of some of the poorer quality foams that are common in the market today. While all memory foams and polyurethane foams in general (including the "green" ones) use some "nasty" materials in their manufacture, some of them have more of this material left in them by the time you sleep on them than others. For those that are sensitive to this offgassing, this can lead to issues ranging from a reaction to the unpleasant smell itself all the way to respiratory issues caused by the vapors. Your best protection against this is to make sure you know who manufactures the memory foam used in a mattress and not just accept the "re-branded name" that has been given to it (and to you). If the foam in your mattress has been certified by Certipur or Oeko-tex (or a similar organization), you can be reasonably sure that at least any smell or offgassing that you may notice has been tested for any potential harm it may cause you (within the limits of the test). More natural materials used in mattresses such as different fibers and good quality latex foam (which may also have a less unpleasant odor for a short time and is usually tested as well) are usually considered to be superior in this area. In the case of Certipur certification, the foam will also have been tested to some degree for durability and so is less likely to lose its beneficial qualities in a few months after purchase but the density of the memory foam would still be much more important durability factor than any limited durability testing done by CertiPur.
Without knowing what specifications and certifications the memory foam in your mattress has, I would not buy it. There are just too many retailers and manufacturers who are more than willing to provide you with this information which gives you the ability to make meaningful comparisons and make sure of the safety of your memory foam to waste any time with those who either can't or won't.
While it's not directly connected to the quality of memory foam itself because higher heat and humidity levels can speed up the softening and break down of any foam material ... with more temperature sensitive materials like memory foam this can happen faster and so I would tend to avoid using memory foam with heated mattress pads or blankets or at the very least use them at the lowest setting and only for short periods of time. In some cases their use can also invalidate a warranty.
So there you have it. Hopefully I have covered the main points of the generic differences, strengths, and weaknesses of memory foam as a whole. In my experience and research, memory foam has been the subject of more misinformation and hype than almost any other material in a mattress and this confusion and misinformation has in my opinion led to too many poor or at least inappropriate mattress buying decisions. It is sometimes a frustrating process to "get to the bottom of things". Memory foam is certainly a valid choice in a mattress material for some people and there are many who love it however I believe that knowing more about what it does in comparison to other materials and why and how it does it, is an important part of buying a memory foam mattress. There are many choices of mattress construction available and the more those choices are based on fact, personal experience, and individual needs and personal preferences, the more likely you will be to buy a mattress that is perfect for YOU.