A combo move is a kind of sport mon attack which can be combined (i.e. executed in the same turn) as another move. Generally, combo moves provide some kind of melee bonus, though they may have other effects that do not depend on being used with a melee attack. The melee bonus of a combo move generally only applies for the turn in which it is executed.
Combo moves are limited to a certain number of uses per battle, generally one to three. (Game-mechanically, this looks like an ammo requirement, though generally combo moves do not require ammo that must be purchased.) Multiple combo moves can be used in the same turn.