humid,dampness,sultry and muggy in climate topics
Humid would be used to describe the amount of water in the air. Tropical climates are generally very humid. Muggy is an informal term used to describe humidity. The proper term may be "It is very humid today" but we will often say "it is muggy out today" or "it feels muggy outside today."
Dampness can be used similarly "it feels damp outside today" but it is generally used for surfaces. "The carpet is damp, my clothes are damp, etc."
Sultry can be used in the context of humidity but you will often only find it in literature. I would say it is more often used for it's alternative definition which is in reference to an attractive person.