There are a lots of sleeping mats on the market but just a few basic types:
Closed Cell Foam Mats: These were the original camping mats, they consist of a thin piece of foam which insulates the sleeper from the ground. They provide some comfort but not very much because they aren't very thick and therefore your body has nothing to sink into. They are very light though, and durable. They can't be punctured - you can cut them to the size and shape you want to shave further weight. They are also quite cheap compared to other mats.
Some closed cell foam mats have been designed with ridges and bumps in order to improve their comfort - see Thermarest Ridgerest and Z-Lite ranges. This works, but only to a degree. Also the insulation value of closed cell mats tends to be lower than other kinds.
Self Inflating Mats: these mats consist of 'open cell' foam sandwiched between two sheets of material - they have a valve at one end which is used to inflate them. When you want them to inflate you lie them down and open the valve - the foam inside then expands and sucks air into the mat - this process can take quite a while and you often have to add a few breaths at the end to get it fully inflated.
These mats are much more comfortable and provide more insulation value than a closed cell foam mat. They can be punctured and also repaired, but finding the leak can sometimes be tricky. They tend to be heavier than closed cell foam mats but have a much smaller packsize.
Airbeds: Airbeds used to be very heavy and were cold to sleep on because the air moved around a lot taking heat from the body. Modern examples are remarkable feats of engineering, they now provide good insulation by keeping the air trapped in pockets and by adding insulation, and they are made from hit technology materials which are both light and durable.
They are much thicker than self inflating mats and so are much more comfortable and they can be made much warmer then any other type of mat by including some form of insulation. Their pack size and weight are generally smaller and lighter than self inflating mats so they are offering a much better night sleep than any other type of mat. One disadvantage of this type of mat is that if it gets a puncture you lose both comfort and insulation - at least with a self inflating mat you have some foam to lie on still.
Other Points: Insulation value can be measured and is called the 'R-Value'. There is more than one system but we've attempted to come up with a figure for each mat (based on the manufacturers specification) that can be used for comparison. A full explanation of 'R-Value' can be found HERE.