Old English box "a wooden container," also the name of a type of shrub, from Late Latin buxis, from Greek pyxis "boxwood box," from pyxos "box tree," of uncertain origin. See OED entry for discussion. German Büchse also is a Latin loan word.
Meaning "compartment at a theater" is from c.1600. Meaning "pigeon-hole at a post office" is from 1832. Meaning "television" is from 1950. Slang meaning "vulva" is attested 17c., according to "Dictionary of American Slang;" modern use seems to date from c.World War II, perhaps originally Australian, on notion of "box of tricks." Box office is 1786; in the figurative sense of "financial element of a performance" it is first recorded 1904. Box lunch (n.) attested from 1899. The box set, "multiple-album, CD or cassette issue of the work of an artist" is attested by 1955.