Some spells, such as the Stun Club (Owl Magic), give you a chance to stun a monster. 
When a monster is Stunned, it stops moving and attacking. A ring of stars appears above its head, along with a countdown showing how long the stun lasts. 
To complete the challenge that asks you to "Use your Wand on a Stunned monster", you have to use your Wand on a monster WHILE it is still stunned.
Note: If the monster is no longer stunned while you use the wand on it, then it WON'T count for the challenge.
Learn more about: Challenge - Defeat X Stunned monsters