Damp is defined as depressed,dejected.
Damping :
Damping is an influence or impact on vibrating system to depress its vibration.
Below is an example figure to understand damping :

Wikipedia definition:
Damping is an influence within or upon an oscillatory system that has the effect of reducing, restricting or preventing its oscillations.
Reference :
https://en.wikipedia.org/wiki/Damping
http://www.bmb.leeds.ac.uk/illingworth/control/