Why is water wet?
Wetness is a feeling, water molecules clinging to a surface and to each other.
Wetness is something you feel, not something water is
A single water molecule is not wet. Wetness is a description of what happens when liquid water meets a surface and spreads across it. Strictly speaking, water makes other things wet, and we feel that contact as a sensation.
Your skin has no dedicated wetness sensor. The brain combines pressure, texture, and cooling into the single tag we call wet, which is why a cold dry breeze can briefly feel damp.
The molecule that wants to hold on
Because the molecule is bent and oxygen hogs the shared electrons, one end is slightly negative and the other slightly positive. This polarity lets water form hydrogen bonds, weak attractions that constantly grab and release neighboring molecules.
Adhesion and cohesion, the two grips
On a surface water likes (glass, skin), adhesion wins and the drop spreads into a film, that is wetting. On a surface water dislikes (a waxed leaf, a raincoat), cohesion wins and the water beads up and rolls off instead.
Why some things never get wet
Hydrophobic materials hold their own electrons too tightly to offer water anything to grab. The drop minimizes contact, pulling into a sphere by its own cohesion. To those surfaces, water never really arrives, so they never feel wet.