Some spells, such as the Snake Bite (Snake Magic), give you a chance of Poisoning a monster. 
When a monster is Poisoned, it turns green. A Venom Vial icon and a turn counter appear in front of it. The counter shows how many times you can draw a card before the Poisoning effect ends.
To complete the challenge that asks you to "Defeat X Poisoned monsters", you must kill a monster WHILE it is still Poisoned. 
Notes: If the monster is no longer Poisoned when you kill it, then it WON'T count for the challenge. While Poisoning is still active, every card you draw deals extra damage to monsters that are Poisoned.
Learn more about: How do I Poison a monster?