c. 1300, "knob or ball attached to another body," especially as used to hold together different parts of a garment by being passed through a slit or loop (surname Botouner "button-maker" attested from mid-13c.), from Old French boton "a button," originally "a bud" (12c., Modern French bouton), from bouter, boter "to thrust, strike, push," common Romanic (cognate with Spanish boton, Italian bottone), ultimately from a Germanic source, from Proto-Germanic *buttan, from PIE root *bhau- "to strike." Thus a button is, etymologically, something that pushes up, or thrusts out.
Meaning "point of the chin" is pugilistic slang, by 1921. A button as a round protuberance you depress to create an effect by closing an (electrical) circuit is attested from 1840s. Button-pusher as "deliberately annoying or provocative person" is attested by 1990 (in reference to Bill Gates, in "InfoWorld" magazine, Nov. 19). In the 1980s it meant "photographer."
late 14c., "to furnish with buttons;" early 15c., "to fasten with buttons" (of a garment,) from button (n.) or from Old French botoner (Modern French boutonner), from boton (n.) "button," which is from the same Germanic source as the English word. Related: Buttoned; buttoning. Button-down (adj.) in reference to shirt collars is from 1916.