Power Steering traditionally works off of a pump that contains hydraulic fluid. The Power Steering pump is powered by a belt driven from the main crankshaft. Some more modern cars are converting to an electric power steering system. Hydraulic fluid from the pump is released into the steering rack to assist turning whenever the steering wheel is turned and the pump is running.
As you turn the steering wheel, the tension put on the steering wheel by your turning is applied to a torsion bar. This bar is connected to the Power Steering Pump and opens or adjusts a valve in the power steering pump that directs pressurized fluid from the pump to push the steering in the direction you are attempting to turn the wheel. The fluid when it reaches the end of its travels returns to the pump.
Since the power steering pump is creating the hydraulic pressure that assists with turning the steering wheel, when it breaks the steering becomes very hard to turn especially at slow speeds or when stationery. This can lead to accidents as instead of being able to make a turn, the car may go straight.
Two common causes of power steering pump no longer working are:
1 - The belt driving it breaks or slips (such as in wet weather). This means the pump no longer gets any power to pressurize the fluid.
2 - A leak causes all the power steering fluid to leak out and the pump no longer has anything to pressurize.