There are two major factors to look for in a new mattress. They are support & comfort.
You don't want the mattress to cause pressure to your body, which causes tossing and turning, which means you wake up tired.
Folding mat comes with two fold benefits. They are folded into a suitcase like form so easy to store and move around. If you don't have that fancy guest rooms, your guest won't complain after sleeping on this mattress. They come with all the comforts a normal mattress should have. You can even carry your own mattress for those slumber parties at your friend's.
The most important factor in finding the correct mattress is proper support. You need the mattress to push up on your body to counteract your body weight. So that means get a hard, firm, stone-like mattress, right? Wrong.
Your body isn't a straight line. Whether you sleep on your back, side, or stomach, your body has curves, and a mattress must come up to support the curves and arches of your body.
The second most important criteria to selecting the right mattress is comfort (or as you may hear it called, pressure relief). If a mattress is too hard, it can cause pressure to your body. This cuts off circulation and pinches nerves (ever wake up with a "pins and needles" feeling in your hand?), and will cause you to change positions frequently.
If you're frequently changing positions, your sleep is fragmented and you don't get into the deeper stages of sleep (such as REM sleep). This means you'll wake up tired, even if you thought you got 8 hours of sleep. When you're trying out the mattress, you should be able to lie in one position without moving around for at least a few minutes. If you can do that, you've found a good mattress.
Those are the two main criteria. If you find a mattress that keeps you in proper alignment which doesn't cause pressure to your body, you've found a great mattress for you. To help fine-tune it from there, there are a few other things to consider.
Most mattresses you're likely to run into are the "innerspring" type. They have metal coils inside of the mattress with foams and fibers on the top. The lower priced mattresses tend to use the older style coil in which they're all tied together. The hourglass-shaped ones are called "Bonnell" coils, but other manufacturers have stronger variations on that type (like the "offset" coil and the "continuous" coil). These are generally a little less expensive than the individually wrapped coil, but don't contour as well and transfer more motion.
The better innerspring mattresses will use individually wrapped coils. This type of coil allows the mattress to contour to your body from the coil level, which give better support and causes less pressure. Additionally, wrapped coils are better at separating motion from side to side on the bed. So if one person bounces around or changes positions, the partner will not feel it as much. The foams above the coils will have varying densities. You can get a mattress with firmer foams on the top or softer foams on the top. Some will be in the style of a "pillowtop" (which means the manufacturer sewed an extra cord around the side of the mattress to indicate it has a good amount of foam).
Foam mattresses are becoming much more popular, and they tend to get higher customer satisfaction ratings than innerspring mattresses (though they might not be what you're used to). There are two major types of specialty foam, and a foam bed will usually have at least one of them, if not both. There is latex, and memory foam.
Memory foam is probably the most recognized type of foam in bedding. It is a slower-response foam (meaning it takes time to return to its normal position). This has the benefit of not causing pressure to the body. Memory foam is perhaps the best pressure-relieving material that is used in beds today.
Latex foam is the other type of common specialty foam. It tends to be more supportive than memory foam, a lot more durable it responds a lot more quickly than memory foam, and naturally keeps a more neutral temperature without relying on gel. However, it does not relieve pressure as well as memory foam does, and isn't as good at separating motion.