How does the hydraulic system work?

It uses an incompressible fluid under pressure to do work. This is a fairly efficient way to transmit the energy over a short distance, and this type of system is capable of great forces. The energy is of course supplied by a pump driven by a motor, or engine (or your foot on the brake pedal). The flow of pressurized fluid is delivered through a control valve to the device that will do the work. This can be a hydraulic motor, or a ram. The motor uses the fluid to deliver a rotary motion. The ram (cylinder) delivers linear motion. The discharge of the device is at a lower pressure and returns to a storage tank (reservoir) which serves as the suction for the pump. Generally, the system should also incorporate some form of excess pressure release so you don't dead-head the pump and break something. This release will dump fluid back to the reservoir.