An insult or insults that are sufficiently offensive to the insulted person that he/she becomes angry enough to start throwing punches.
Person 1: Too bad your mama didn't drown you when you were born, you worthless nigger/kike/camel jockey/bitch/cracker/gook/insert chosen offensive word(s) here!
Person 2: I'm gonna beat your ass! Them's fightin' words!
words that are designed to or are capable of provoking violence
It's one thing to argue, but these ar fightin' words