Damage is one of the two stats that are written on a Character's card, along with Power. It determines how much Life the card will remove if and when it wins one of the four rounds. For example, Pan is a character with 3 Damage, therefore the opponent's life count will drop from 12 to 9. The goal of the game is to either have more health than your opponent by the end of the 4 rounds, or KO them (by bringing their life count down to 0) before they do unto you.
Abilities and Bonuses.
Other cards have Abilities that reduce the enemy's Damage, such as Alexandrea or Uranus. These cards are called Damage reducers. The Pussycats clan has a Bonus which reduces the enemy's damage by 2, to a minimum of 1.