Altercation is a nicer word for "quarrel," which is a nicer word for "fight."
Fight is a simple, effective one-syllable word, while quarrel is a softer, two-syllable word, and altercation is a very civilized-sounding four-syllable word for the same uncivilized thing: a noisy argument between angry people. Someone who gets a black eye fighting for a parking spot might — after cooling down — describe the incident as an altercation rather than as a knock-down, drag-out brawl.