It seems Attack Power works the same way as Spellpower, so I guess I'll try to explain it the same way.
Strength (and agil?) from gear, based on class, give you a certain attack power. Attack power in turn works with a coefficient from the specific ability you're using to do a certain amount of damage.
PVP Power, I think...I don't have beta...., increases your overall damage from an ability by a set amount based on the amount you have. So maybe 100 attack power gives you a 10% increase on damage.if your move would have done 20k, based on the ability damage (which was based off attack power), it'll do 22k because of the PVP power.
Of course I don't play melee or have beta so remember, it's all just a guess sort of.