What happens when something is damped? When two parts move relative to each other or to a material which contacts both and this movement is reduced due to friction, then that is damping. The energy which previously caused the movement is converted to heat.
Vibration is sometimes desirable (as in a cartridge or a speaker drive unit), and sometimes undesirable (almost everything else).
And at certain frequencies, objects which vibrate can also resonate, which can lead to excess movement.
Damping only works when the part to be damped is coupled to the damping medium, which then can move relative to the part to be damped, and the damping medium is coupled to the air, or another part which usually has more mass.
Note that over-damping can only occur in a situation where vibration is intentional.
If a structure is not intended to vibrate it should have all its potential resonances eliminated, otherwise it will transmit vibration at some frequency or other if it is exposed to that frequency or frequencies near it. This will interact with the signal and change it, introducing distortion.
