Hydraulics in cars take advantage of a two-cylinder system connected by a pipe filled with an incompressible liquid. When force is applied to one cylinder, the other cylinder raises up, no matter how far apart they are.
A basic hydraulic system consists of two cylinders, a master and slave, that can be forced down using a connected pipe. This pipe and bottom of the cylinders are full of an incompressible fluid, typically an oil, that allows the force to be transferred through the oil in the pipe to the other cylinder causing it to rise. No matter what shape or length of the pipe, the force is still conserved, and the slave cylinder is forced upward. This action provides the force to raise a car, run an amusement ride, operate breaks and many other functions.
The concept of trading force for distance is a common way to gain leverage in mechanical systems; the same concept that allows hydraulics to function is used in ramps and pulley systems. If the slave and master cylinders on the hydraulic were identically shaped, no mechanical advantage would be achieved and the hydraulic would serve no practical purpose. The multiplication of force required to lift cars and other jobs that require hydraulics comes from altering the shape of the cylinders. By making one cylinder long and thin and the other short and fat, the base area of the cylinders is changed. With the master cylinder shorter, its base area increases, and the slave cylinders area decreases making it a longer shape. This means when the master cylinder has force applied to it, the force is multiplied when the slave is forced out because the same amount of force is being exerted over a smaller area.