The dampness that forms in your mouth when you smell something delicious is drool. When it actually drips from your mouth, you drool.
The official term for drool is saliva. Babies drool, dogs drool — we all drool sometimes. Sometimes people drool (or salivate) because of problems with their salivary glands. You might drool when you skip breakfast and your friend offers you a warm, homemade cinnamon roll. The word comes from drivel, which today means "speak nonsense," but originally had the sense of "to slobber or run at the nose."