mid-13c., "division, portion of a whole, element or constituent (of something)," from Old French part "share, portion; character; power, dominion; side, way, path," from Latin partem (nominative pars) "a part, piece, a share, a division; a party or faction; a part of the body; a fraction; a function, office," related to portio "share, portion," from PIE root *pere- (2) "to grant, allot."
It has replaced native deal (n.) in most senses. Meaning "an allotted portion, a share" is from c. 1300; that of "a share of action or influence in activity or affairs, role, duty" is by late 14c. The theatrical sense (late 15c.) is from an actor's "share" in a performance (The Latin plural partis was used in the same sense). In music, "one of the voices or instruments in a concerted piece" (1520s). Sense of "separate piece of a machine" is by 1886. Meaning "the division of the hair on the head when dressing it" is by 1890, American English; the earlier word for this was parting (1690s).
As an adjective from 1590s. Late Old English part "part of speech" did not survive and the modern word is considered a separate borrowing. Phrase for the most part "most, the greatest part" is from late 14c. To take part "participate" is from late 14c.