Answer
In pressure cooker, water boils at a higher temperature when pressurized. In an open pot, the water never gets hotter than $100^{\circ}C $(less at higher altitudes). In a pressure cooker, higher temperatures are reached and therefore the food cooks faster.
Work Step by Step
In pressure cooker, water boils at a higher temperature when pressurized. In an open pot, the water never gets hotter than $100^{\circ}C$ (less at higher altitudes). In a pressure cooker, higher temperatures are reached and therefore the food cooks faster.
Pressure cooker doesn't allow for anything (even gases) to escape at any significant amounts (unless the pressure inside gets too high and you hear that whistling noise). With heat, the gases inside want to expand, but because they are restricted to the volume of the pressure cooker they can't, so pressure builds up. In addition, when a liquid, lets say water in this case, is heated under normal pressure its temperature won't go above $100^{\circ}C$, because any water molecule that has higher energy leaves the liquid and goes into gas phase. Now, applying pressure to water, will increase the boiling point (for example from $100^{\circ}C$ to $110^{\circ}C$) Reason: When any liquid is under higher pressure it is less likely to go in the gaseous phase. The pressure cooker works with these principles, because usually when you cook water in an open pot, the boiling point of water restricts the temperature to a $100^{\circ}C$. A pressure cooker uses the pressure to keep the water in the liquid form even though it is far above the boiling point, and hence the temperature is far above $100^{\circ}C$. Because the pressure build up inside causes higher cooking temperatures thus reducing cooking times
