Curse is an attachment card type. Curses are played on enemy units and remain in play until the unit dies or another spell or effect removes the curse. Cursed Relics are a separate card type; these also count as Curses, but are played on the enemy player.
Curses and cursed relics are blocked by Aegis on the targeted unit or player.
There are some "curses matter" cards which give a benefits from playing curses, such as Malediction Reader and Skywalk Enforcer.