The healers charge 5 gold per level per hit point to heal you. If you're short on cash, they'll heal as many HP as you have gold for. If you have exactly the gold you need to be healed, then for some reason nothing happens. Get more gold and then they'll heal you.
If you go to them when you're fully healed, they'll shout "You look fine to us!"
If you have greater than your max hp, (possible via "JENNIE" codes) then you can sell your excess hp to the healer's hut.
Other Uses Edit
If, at the start of the game, you find yourself with VD (must have more than 50 lays), you'll be dropped to 1 HP and need to visit the Healers right away, or even Violet kicking you in the groin might kill you.
If you play a female and have a pregnancy appear as soon as you log in, you'll automatically go to the Healer's hut. Nathan the Healer will deliver the child and tell you its gender, and you get to name it.