button (n.) Look up button at Dictionary.com
c.1300 (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," common Romanic (Spanish boton, Italian bottone), ultimately from Germanic (see butt (v.)). 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 something you push 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."
button (v.) Look up button at Dictionary.com
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.). Related: Buttoned; buttoning. Button-down (adj.) in reference to shirt collars is from 1916.