They are similar to Power Types, but they react to Weapon Classes. If you're using a wrong Weapon Class when encountering an enemy character, you will get penalized (your attack power will be reduced) by approximately 10%. Each enemy class reacts to only one weapon class.
For example, if a lvl 42 player uses a weapon with 87 attack power (87 + 14 lvl bonus = 101 total attack power) against the wrong enemy class, his attack power will be reduced by 11 (101 * 0.1 = 10.1).
Note how this penalty applies to the sum of the weapon's attack and the player's bonus attack level.