Originally Posted by
Tokee
Attack Power was a weird stat budgeted onto items from Vanilla and BC. It bridged the gap between STR users and AGI users. Barbarous Blade, Arcanite Reaper, and Ash'kandi are notable examples of Vanilla WoW weapons that were useable by hunters, shaman and other melee in vanilla that were quite good.
Strength and Agility equated to attack power on the statistics page for the corresponding classes, but I believe for its time it was cheaper than the primary stats for item stat budgeting.
It's a relic of the past. Once you get out past BC content you won't see it much at all. It won't be on any item once you get to Cataclysm zones and beyond.