Different materials have different levels of elasticity. Up to a certain point, they can be deformed and released, and they will try to return to their original condition.
Beyond that point they stay deformed.
With some materials, if it returns to its original state too quickly, it can produce a bouncing effect called an oscillation.
Preventing or reducing this oscillation is called dampening. It can occur in many different ways. The dampening material absorbs the energy from the oscillation.
In vehicle suspension, a shock absorber reduces oscillation in the spring.