The basic principle is that food cooks faster at higher temperature.
The governing law in Physics is Gay-Lussac's Law: The Pressure Temperature Law. This law states that the pressure of a given amount of gas held at constant volume is directly proportional to the Kelvin temperature. As the pressure goes up, the temperature also goes up, and vice-versa.
Since the pressure cooker is made of heavy gauge aluminium or stainless steel, and the both the pressure-release (or 'weight') vent and the safety vent are closed, the volume stays constant even when the pressure rises due to heating. This causes the temperature of the steam also to rise. If the vents were open, steam would have escaped, releasing pressure and preventing the temperature from rising. As opposed to steam at slightly above 100degC in a vessel with a loosely fitting lid, the steam in the closed pressure cooker is usually slightly higher than 121degC (pressure is 15psi above atmospheric pressure at sea level). This causes food to cook at roughly 1/3 the time required to cook in simply-covered vessels.