Weapon that have a certain Power Type will give an approximately extra 25% attack bonus when used against certain Family Types (see the table below). They exist to provide a boost to the player when pitted against the right Family type.
|Fire||burns Beast||cleanses Dark|
|Ice||seizes Construct||freezes Humanoid|
|Shock||paralyzes Beast||disrupts Construct|
|Arcane||dispels Dark||zaps Humanoid|
|Mining||extracts Resource *|
* Mining power type works somewhat differently. Not only you'll recieve the 25% attack bonus, but these weapons are also the only ones which can be used to "defeat" (extract) the resources. If you're not using a Mining weapon and you encounter a resource, your attack power will be reduced to 1.
For example if you use an Arcane weapon you will get a 25% attack bonus (rounded up to the nearest whole number) against Dark and Humanoid characters. This bonus applies to the sum of the of the weapon's attack and the player's bonus attack level.
For example, a level 12 character with a power 22 weapon gets a bonus of (22+4)*0.25=6.5 which is rounded up to 7. Which means you get a bonus of +7 attack if the power type effects the family type of the enemy you are in combat with.