If you go to the Sorceress' Hut, you can click on her hat. She then offers to sell it to you for 1,000,000,000 lollipops. What does it do?
The Sorceress Hat enhances the effects of your spells and potions. The only effect I have seen so far is to double the amount healed by the health potion, although I am currently experimenting to determine the effects on other potions/spells.
Healing potion: Increases amount healed from 100 -> 200
Black Demons: Increases damage from 750 -> 1200
Anti-gravity potion: Increases flight time by a factor of ~1.5