Attack power is mostly a combination of commander accuracy and fleet attack attributes, but also is affected by Gems/Commander Ablilities/Hull Type and Weapon Type, it is a attribute of each Commanders fleet and the value is derived from a combination of commander stats and fleets stats. It is countered by opposing commander and fleet stats, such as dodge and ship/fleet Defence & Agility, it can be enhanced directly with gems and indirectly with steering attribute/Weapon power/other gains.
(see also Combat Mechanics)