Some spells, such as Voodoo Queen (Water Magic), give you a chance to Curse a monster. 
When a monster is Cursed, it turns purple. A Voodoo Doll icon and turn counter appear in front of it, showing how many cards you can draw before the effect ends. 
To complete a challenge that asks you to “defeat X Cursed monster", you must kill a total of X monsters WHILE they are still Cursed.
Note: If the monster is no longer cursed when defeated, then it WON'T count toward the challenge.
Learn more about: How do I Curse a monster?