Remember 殴る, which means "to punch"? Well, add on 合う and you've got punches that have come together with other punches. By "come together" I mean your fist is coming in contact with someone's face, and their fist is coming in contact with your kidneys. In other words, this is a fistfight.
The readings come from 殴る and 合う, punched together.
My man is in the middle of the fist fight in the club.