In a pressure cooker, the cooking is fast because

For faster cooking, we need water in liquid form at high temperature, much above its boiling point.

In a pressure cooker, steam is built which is not allowed to escape. This increases pressure inside the cooker which increases the boiling point of water. Thus water remains in liquid state even at temperatures well above ${100}^0\mathrm{C}$. Thus very hot water supplies heat to food contents 

If pressure was not built up, then water would boil and escape away at ${100}^0\mathrm{C}$..