Wands are used to clear fog and open up new areas on the board!
Each area will require a certain amount of Mana to unlock. Once you're at the appropriate level, you can see just how much Mana is needed for that area!
Tap on wands to add them to your Mana Counter at the top of the screen. When you have collected enough Mana, you should be able to unlock the next area on the map!