Pressure cookers are a great solution to cooking foods quickly while simulating the effects of a long braising process. It works roughly according to the ideal gas law, PV=nRT. Although the ideal gas law has limitations in regard to application in the real world, the principles behind it are applicable to the pressure cooker. The machine works as follows, a liquid inside is brought to a boil. This boiling liquid changes states of matter and becomes a gas. Because the gas is limited by the volume of the pressure cooker, V remains constant. The trapped gas increases the internal pressure of the container and without adding or subtracting any particles, n remains constant as well. R is constant at 8.314J/molK, so for the equation to remain true the increase in pressure results in an increase in temperature greater than that of an open container in which the volume the gas can occupy is much greater. This increase in temperature allows for the food inside to cook much faster.
Interestingly, cooking at high altitudes can often be challenging since the lower atmospheric pressure makes cooking time longer. A pressure cooker can account for this since it compensates for some of this loss of pressure. It is still under the physics of pressure, but can give you a couple more minutes back when you are cooking a nice warm dinner after a night of skiing in the mountains.