The adjective "damp" describes the presence of water– but not a lot of water. We usually use "damp" for objects made of cloth, the ground, and the air. It’s similar to the adjective "moist."
There’s a damp towel hanging on the towel rack.
The ground is damp because it rained last night.
The air felt damp after it rained.
Our house feels damp because of the high humidity.
It’s not a good idea to leave the house with damp hair in the winter.
Her hair is damp because of the rain.
The word "dampen" is a verb. To dampen something is to make it wet, but it also means that something is reduced or made less.
simple
past
past participle
dampen
dampened
dampened
The woman dampened the towel with cold water and applied it to her forehead.
I hate to dampen your spirits, but it looks like we aren’t going to make our goals for this quarter.
Our expectations for a successful event were dampened by the weather.
