A condition of being moist, watery, or damp is wetness. Even if it's barely raining as you walk from the bus stop, the wetness of your shirt might make you want to change your clothes once you get home.
Wetness is caused by some kind of moisture, whether it's the wetness on your cheeks as you watch a really sad movie or the wetness of your bathing suit after you swim across the lake. The wetness of your basement means it's not a good place to store books and papers, and the wetness of the spring — one rainy day after another — means the summer will be lush and green, and you're likely to see moisture-loving mushrooms popping up everywhere.