plural of man (n.). In common with German Männer, etc., it shows effects of i-mutation. Men's liberation first attested 1970. Men's room "a lavatory for men" is by 1908, American English. Earlier it had a more general sense:
men's room, n. "One end of this [cook and dining] room is partitioned off for a men's room, where the crew sit evenings, smoking, reading, singing, grinding their axes, telling stories, etc., before climbing the ladder to their night's rest in the bunk room ... For many years women have been employed in [logging] camps as cooks, hence the name men's room, for the crew are not allowed in the cook room except at meal time." [quoted in "Some Lumber and Other Words," in Dialect Notes, vol. II, part VI, 1904]
Menswear (also men's wear) "clothes for men" is by 1906. To separate the men from the boys in a figurative sense "distinguish the manly, mature, capable, etc. in a group from the rest" is from 1943; earliest uses tend to credit it to U.S. aviators in World War II.
One of the most expressive G.I. terms to come out of the late strife was "that's where they separate the men from the boys" -- so stated by American aviators leaning from their cockpits to observe a beach-landing under fire on some Pacific island far below. ["Arts Magazine," 1947]