Damping arises from the removal of energy by dissipation or radiation.
Damping is very important in controlling vibratory motion such as mechanical oscillations, noise and alternating electric currents.
A swing stopping on its own, a simple pendulum slowing down, etc. happens because of damping.
Importance of damping
Consider a system of a boy throwing a ball, the ball, rolls through the ground and stops at some point of time due to friction, which is a kind of damping.
If there was no damping the ball will not stop its motion and will continue to move till some other force stops it.