How does pressure cooker work? If you increase the pressure, the boiling temperature increases as well. In the other direction: if you decrease the pressure enough you could even make water boil at 18 dergees C.
However I met this strange thing in my wifes kitchen called "pressure cooker".
I don't understand how you can cook things quicker with that. If you increase the pressure inside this tool, you are just increasing the cooking temperature. And thus nothing will even boil.
What did I misunderstand?
 A: First consider a pot with a loose lid over it. As the temperature rises, the vapor pressure of the steam rises as well (even before boiling) and the steam will push its way out under the lid. You'll get cooking temperatures over 100C, but not by much, and a lot of the energy you expend on cooking just goes out into the air instead of into your food. And to add insult to injury, your lid will rattle around on top of the pot.
Now consider the pressure cooker. The lid is well sealed and tightly locked down. The vapor pressure rises with temperature as before, but now it has nowhere to go; the pressure can't relieve itself by pushing the lid up and escaping. The energy you put into heating the food and water stays in the pot, and consequently you can achieve higher temperatures inside the pot. In fact, the "pressure" part of a pressure cooker is only a side effect of trapping the hot gasses inside the pot; the real benefit is the higher cooking temperature.
A: Think of it like this:
Assume that you want to make pasta. For a piece of pasta to be "cooked" a certain amount of energy has to be given to it (depends on the type of pasta) (also as anna v mentioned It is the energy that changes the molecular bonds that results in cooking and the higher the temperature the faster). The way to transfer this energy to it is by putting it inside hot water. The choice of boiling is actually because the hotter the medium the quicker the energy transfer. I am pretty sure that you can make pasta even at lower temperature than 100 oC, but will need more time.
Now, the classic way of doing it is by using a traditional cooker, where water is boiling very close to 100 oC (as Asher mentioned, it might be a bit over with the lit on, or may be because of impurities (salts)). If you choose to cook your pasta in a pressure cooker then what actually happens is that by increasing the pressure (the way Asher described) you increase the boiling temperature of the medium and thus the rate over which the transfer will occur, which will result to much (I haven't tested it but I think it is much much much) faster cooking.
Attention, you do not violate thermodynamics, you just take advantage of what we know.
Warning, I wouldn't test it with pasta because it already needs a small amount of time to make it! I would try it  on a food like stew maybe.
A: Also, though this might not be an actual use for this, you could make steak very rare with it. 
In the case of a very rare steak, you need it to be cooked just enough to make it safe, kill bacteria, and make it easier to digest, but no more than that. If you put it high pressure, you could heat it up to a high temperature without cooking it. That way, you sterilize the steak and cook it just enough, but without cooking all the way through. 
