Power steering was invented to make it easier to turn the steering wheel at low speeds or when stationery. It was initially invented to help drivers of large heavy vehicles. If you get in a car that does not have power steering it will generally have a larger diameter steering wheel to make it easier for the driver to turn. When power steering fails, it is very hard to turn the steering wheel. This can be experienced by trying to turn the steering wheel with the engine off (unless it is a modern car with electrical pump in which case, the pump may activate).
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.