A damper on a car is also known as a shock absorber. Without a dampening structure, the car spring extends and releases the energy it absorbs from a pot hole or bump at an uncontrolled rate. This means the spring would bounce until all the energy is used up.
The shock absorber controls the unwanted spring motion though dampening. Shock absorbers turn the kinetic energy of the vibratory motions into heat energy that is dissipated through hydraulic fluid. When a car hits a bump, causing the spring to coil and uncoil, the energy is transferred to the shock absorber through the upper mount and down through the piston rod into the piston. Tiny orifices perforate the piston and allow a small amount of fluid, when under great pressure, to pass through. This slows down the piston and also the spring.