A shaman hut is a explorable location where you can cleanse your followers of their ailments, heal their injuries and physical ailments, or barter for exotic scrolls, mushrooms and other mystical-focus items.
Cleansing a character will rid that character of all negative mental perks. A cleansing will require an offering of your supplies and can be expensive. It is typically a good idea to check the shaman's trade inventory for green mushrooms first, as the cost of barter is much lower - two green mushrooms can often by traded for the price of a single cleansing.
Healing a character brings them up to full health completely, removing their injured status along with any physical ailments such as infected wounds and diseases they may have. Healing costs the same as cleansing.