The attack power skill represents your ability to deal physical damage, while most races and professions start with some limited natural attack power the bulk of your ATTACK POWER rating will come from wielding weapons.
The higher the skill the more damage you can potentially deal.
Formula
Damage Dealt + (ATTACK POWER / 20)
This skill is used in conjunction with your Weapon skills but is not limited to any one weapon type.
Your actual damage is limited by your DPR and any style you`re using.