Green’s Dictionary of Slang

1. mid-19C one who occupies a box at the theatre, opera, etc.

1853		N.Y. Clipper 23 July 2/4: ‘The “boxers” of the Bowery and the National have a semi-sensual look; the “ladies” are either ignorant servant girls, or those who live by selling their desires’.
1869		Sporting Gaz. 25 Dec. 923/2: Their [i.e. two plays] freshness will scarecly be tarnished in the eyes of the most fastidiousness ‘boxer’.

2. (Aus., also bocker) a low-crowned felt hat.

1900		Bulletin (Sydney) 14 Jul. 13/3: Then he arose, intending to put on his tall silk hat – and found in its place only the brimless boxer of the obvious imposter!
1911		E. Dyson ‘Dukie M’Kenzie’s Dawnce’ in Benno and Some of the Push 39: Somebody knocked his boxer from its peg, and walked in it.
1925		Sydney Mail 15 July 8/1: It was the time of the ‘bowler’ hat, the ‘boxer,’ the ‘hard-hitter,’ the ‘plug hat,’ the ‘derby’ — terms synonymous, but varying according to environment.
1942		Le Courrier Australien (Sydney) 5 June 7/1: You call a bowler hat a darby or hardboiled hat: we line it up as a boxer, bocker, hardhitter, eggboiler, plug hat, peadodger, bun or hap harry.

3. a tall hat, a top-hat.

1984

Partridge DSUE (8th edn) 127/1: ca. 1880–1910.

4. (US tramp) a boxcar.

1927		‘Jargon of the Und.’ in DN V 440: Boxer, A box car.
1931		Irwin Amer. Tramp and Und. Sl. 36: boxer.–A box car.