The word "damp" is an adjective that means wet or moist.
a damp sponge
The sponge remained damp several hours after it was used to wash the car.
The air feels damp outside today.
The basement is damp after a heavy rain.
Whenever the grass remains damp for several days, mushrooms suddenly appear.
mushroom
The cold, damp air inside the cave made everyone feel slightly uncomfortable.
She put a cool, damp towel on her forehead to relieve a headache.
The word "dampen" is a verb:
She dampened a towel with cold water and put it on her forehead.
The grass was dampened by the morning dew.
Their hopes for a win were dampened by the other team’s surge of energy in the fourth quarter. (To dampen also means to lower a person’s expectations for a good result.)
