It's the Bombard stat. Some units can use it as an active ability, and the maximum number of hit points they can take off from the unit they bombard with one use of the ability is called the Rate of Fire (ROF). To nerf artillery a bit, some units can use 'lethal bombardment', i.e. they can kill the target if they take enough hit points, but the rest have their ROF capped at the target's number of HP minus one.
The number of times you can use a unit's bombard ability is the same number of 'normal' attacks you could make with it.
As a passive ability: if a unit attacks a tile in which there is a unit with bombard ability other than the one being attacked, the unit with bombard will first use a bombard attack (assuming that it hasn't used up all its movement points) and then the fight will go on.
The Escape from Zombie Island series of scenarios uses this mechanic to completely rework how Civ is played: hordes of Zombies attack your units, who shoot them and retreat.
The AI is notoriously poor at using the Bombard ability, though, except with planes.