Something that's damp is slightly wet or soggy. If your shoes are damp when you enter your friend's white-carpeted house, you should probably take them off.
Damp things are moist. Your lawn might be damp with dew in the morning, and if it's supposed to rain lightly, the weather report might include the word damp. Sometimes damp is a noun, as when your grandmother warns, "Don't go out in the damp without your umbrella!" To damp is to hold back, make soft, or restrain: "Use your hand to damp the sound of the cymbal after you hit it with the drumstick."