Card breaks only apply to the card-based battle system of Kingdom Hearts: Chain of Memories and Kingdom Hearts Re:Chain of Memories. All cards have a certain value, which may be nullified, or "broken", by a card of equal or greater value. Cards may also be broken by another card with a value of zero. Most often this is used to break Sleights (three cards stocked together to produce certain combat moves or a higher card value).
However, neither combatant will attack if both play with equal numbered cards, which results to a very quick temporal stun for the one who played the card first. In Re:Chain of Memories, if Riku acts quickly enough in breaking an opponent's card, he gains a boost in attack power.