The official definition is “to decrease, in amplitude, an oscillation of any kind.”
When refereeing to suspension, damping is correlated to either rebound or compression damping. In short adding damping is to inhibit the flow of oil which will affect either compression or rebound. i.e. adding compression damping makes it harder to compress suspension -or- adding rebound damping makes returning to full travel slower.
Damping SHOULD NOT be confused with dampening. Dampen – “to make slightly wet”