A Class Bonus is when a Champion of a certain Class is paired up against a Champion whose Class is weak to it. A Class Bonus can increase and decrease Hero Rating, as well as Attack power.
Every Class has a Class Bonus.
List of Class Bonuses
Currently, the Class Bonus system goes like this:
Cosmic 
is strong against Tech, Tech 
is strong against Mutant, Mutant 
is strong against Skill, Skill 
is strong against Science, Science 
is strong against Mystic, Mystic 
is strong against Cosmic.