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."