Dampening is a technique where the right hand rests on the strings near the bridge resulting in a muffled sound when the string is played with the pick.
Place the base of your right hand on the bridge as shown in the photo below. Your hand should also be resting on the string (or strings) as close to the bridge as possible.
Dampened notes are indicated by a curved line with a "D" written above it as in Lick 21 below.