We have three words to describe concepts on the scale between 'wet' and 'dry', but they are used very differently.
1. Humid/humidity.
This term applies only to climate and atmospheric conditions. It is a combination of warmth and a high proportion of water droplets in the air. The Amazon rainforest, for example, is humid. The reason you haven't heard native speakers say 'humid' is because it has this restricted use. It's a false friend for speakers of Latin languages.
2. Moist/Moisture
'Moist' is the opposite of 'dry' for many objects, usually in a positive sense. For example, 'moist skin' is softer to touch than dry skin, a 'moist cake' is nicer to eat than a dry cake, 'moist soil' will help plants grow better than dry soil will.
3. Damp
'Damp' suggests cold and wet, and is often negative. A house which is badly insulated may be damp. If your clothes get wet in the rain and you don't dry them properly, they may still be damp the next day - it isn't a pleasant sensation to wear damp clothes. Weather, especially in the British Isles, can be described as damp - not exactly wet, but cold and with a lot of moisture in the air. This is, in some ways, an opposite of 'humid'. The atmosphere in the warm rainforest is humid, while the atmosphere in the cool British Isles is often 'damp'.