A creature or character that is Cursed will endure a primary stat reduction of -25, including Luck.
Being Cursed persists after the end of combat, and lasts until the curse is removed.
List of Curses
Each Curse will have its own name, signifying the stat which is reduced.
Using the Blessing service in town will remove all curses.
Equipping an item which provides immunity to being Cursed will not remove any existing curses from that character, nor will leveling up. A player that is resurrected will no longer have any prior curse(s).
There's a nomenclature pun here, since curses are not to be confused with Hexes, which are an entirely different thing.