Mastery is a sub-section of the destiny board, that improves your combat abilities with spells and armor.
Mastery should not be confused with Specializations. Mastery of a specific tree (e.g Pyromancer) allows the player to use higher Tier weapons and armor of that tree. Weapon mastery also rewards the player with extra active and passive Abilities. Specialization improves a specific gear's or item's Item Power greatly. See Specializations for more information.