Cooking with a pressure cooker uses the principles of various gas laws, but specifically the Gay-Lussac's Law. This law states that the pressure of a system and the temperature are directly related; that is, if we can increase the pressure of a given system, the resulting temperature will be higher than that of a system with lower pressure but the same heat applied.
Using a pressure cooker takes advantage of this fact. A pressure cooker is essentially a strong, well-sealed pot. It has a very small vent for safety, but the pressure inside the cooking area is increased as the liquid inside turns to steam. The temperature of the fluid inside is raised to higher than boiling (212 degrees F.), higher than what could be reached in a saucepan, with the result that the food inside cooks more quickly.
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