The gem-like tiles on the gameboard are Adventure Time items encased in amber.
Match 3 or more of the same color/shape to remove them from the gameboard. As you make matches, your character will attack enemies. Creating combos (multiple, 3 or more of-a-kind matches) will increase your character's attack power.
Matching tiles will also fill up your Special Meter so you can use your Special Abilities during battle.