Damping is another word for friction. It's most commonly used in connection with oscillations. For example, a pendulum, once set in motion, does not continue for ever because of frictional forces. We say the motion is damped.
Springs in a car suspension help soften the effect of the bumps in the road. However, they are damped to stop the car bouncing up and down too much and making everyone seasick.
Coefficient of Restitution is a measure of how much kinetic energy is lost when objects collide. It expresses how elastic or inelastic a collision is.
A search on Google will find further information on both of these.