Another name for the battle is the climax, it's the point in the story where the tension reaches its peak. For example, if two characters are arguing in a short story, the argument becomes so heated that it crosses the line from the verbal to the physical and one character punches the other. The battle is absolutely vital in changing the protagonist from the kind of person he was at the beginning of the story to the kind of person he is at the end.
The battle doesn't have to be an epic clash like you'd see in The Lord of the Rings. In fact, I've noticed that my favorite battles in fiction are fairly quiet and revolve around a few core characters.
In Full Metal Jacket, the battle in the first half of the film in Parris Island is when Pyle kills Hartman and then commits suicide because it crosses that line I just mentioned, going from verbal abuse to physical violence. In Vietnam, this is shifted from physical violence to verbal as Joker confronts his true enemy Animal Mother and the two argue over whether they should kill the Vietnamese sniper that attacked their squad or leave her to bleed to death from her wounds. Joker's argument for a quick death prevails.