Axie Infinity battle follows a Rock-Paper-Scissors method for the class bonuses and penalties. Similar to Pokemon with their types. Below is the illustration of how it works.
The class bonus and penalty works by playing CARDS CLASS against the BODY CLASS of opponent's Axie. Example:
On top of that, there is also additional 10% bonus on attack and shield when an Axie uses cards from the same class. Card Class and Body Class bonuses are stackable. Example: