noun : a usually brief and disorderly struggle or fight : scrape, scuffle
This word has its origin in rugby: scrum in its earliest use refers to the process in rugby by which the ball is put into play, with forwards from each side coming together in a tight formation and struggling to gain possession of the ball (using their feet) after it's been tossed in among them. Scrum is short for scrummage, which is synonymous with the rugby scrum and is also a verb: in a scrum, or scrummage, the players scrummage.
Scrummage itself is an alteration of scrimmage, which is used with both rugby and American football meanings. Neither game is for the faint of heart; that a word related to both could give us a term like scrum is no surprise. Scrimmage, though, didn't start with sport. Its earliest meanings are "a minor battle" and "a confused fight." It comes from the same source as the word skirmish.