"seat on which the driver of a coach sits," 1650s, from coach (n.) + box (n.).
Entries linking to coach-box
coach n.
1550s, "large kind of four-wheeled, covered carriage," from French coche (16c.), from German kotsche, from Hungarian kocsi (szekér) "(carriage) of Kocs," village where it was first made. In Hungary, the thing and the name for it date from 15c., and forms are found since 16c. in most European languages (Spanish and Portuguese coche, Italian cocchino, Dutch koets). Vehicles often were named for the place of their invention or first use (compare berlin, landau, surrey). Applied to railway passenger cars by 1866, American English. Sense of "economy or tourist class" is from 1949.
Meaning "instructor/trainer" is c. 1830 Oxford University slang for a private tutor who "carries" a student through an exam (compare pony in the student slang sense "translation"). Transferred sense in sports, "person employed to train athletes for a contest" is attested from 1861. A more classical word for an athletic trainer was agonistarch, from Greek agonistarkhes "one who trains (someone) to compete in the public games and contests."
All panelled carriages with seats for four persons inside, and an elevated coachman's seat, are designated coaches. The town coach proper, has windows in the doors, and one in each end, the quarters being panelled. [Henry William Herbert ("Frank Forester"), "Hints to Horse-Keepers," New York, 1859]
box n.1
"rectangular wooden container," usually with a lid, Old English box, also the name of a type of shrub, from Late Latin buxis, from Greek pyxis "boxwood," pyxion "writing table, box," made of boxwood, from pyxos "box tree," which is of uncertain origin. Beekes suggests a loan-word from Italy, as that is where the tree is native. Dutch bus, German Büchse "box; barrel of a gun," also are Latin loan-words.
The meaning "compartment at a theater" is from c. 1600 (box seat in the theatrical sense is by 1850). The meaning "pigeon-hole at a post office" is from 1832. The meaning "television" is from 1950 (earlier "gramophone player," 1924). The meaning "station of a player in baseball" is from 1881. The graphics sense of "space enclosed within borders and rules" is from 1929. The 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 the notion of box of tricks. Box lunch (n.) is attested from 1899. The box set "multiple-album, CD or cassette issue of the work of an artist" is attested by 1955. To think or act outside the box "contrary to convention" is attested by 1994.