early 14c., originally in legal sense of "to call" to a higher judge or court, from Anglo-French apeler "to call upon, accuse," Old French apeler "make an appeal" (11c., Modern French appeler), from Latin appellare "to accost, address, appeal to, summon, name," iterative of appellere "to prepare," from ad "to" (see ad-) + pellere "to beat, push, drive" (from PIE root *pel- (5) "to thrust, strike, drive").
Probably a Roman metaphoric extension of a nautical term for "driving a ship toward a particular landing." Popular modern meaning "be attractive or pleasing" is attested from 1907 (appealing in this sense is from 1891), extended from "address oneself in expectation of a sympathetic response" (1794). Related: Appealed.
c. 1300, "proceeding taken to reverse a decision by submitting it to the review of a higher authority," from Old French apel "call, appeal in court" (Modern French appel), back-formation from apeler "call upon" (see appeal (v.)). Meaning "call to an authority" is from 1620s; that of "attractive power" attested by 1904.