c. 1300, sceu, schewe, "act of exhibiting to view," from show (v.).
The meaning "an elaborately prepared display or spectacle to entertain a crowd" is recorded by 1560s. That of "an exhibition of strange objects, trivial performances, etc." is by 1760, hence "any kind of public display or gathering" (by 1830). The sense of "entertainment program on radio" is by 1932, later of television.
The sense of "appearance put on with intention to deceive" is recorded from 1520s. That of "ostentatious display" is from 1713 (showy is from 1712). The meaning "third place in a horse race" is from 1925, American English (see the verb). In military slang, "battle," by 1892 (Kipling).
Show of hands "raising of hands as an indication of the sense of a meeting, etc." is attested from 1789; Phrase for show "for appearance's sake" is from c. 1700. Show business is attested from 1850; the short form show biz turns up in Billboard magazine by 1942. The actor's creed the show must go on (scil. despite difficulties or calamities) is attested from 1890. Show-stopper "act that wins so much applause as to pause the show" is by 1926; show trial for one likely prejudiced and pre-judged, but done nonetheless with great publicity, is attested by 1937.