late 14c., "to bring to an end;" mid-15c., "to come to an end" (intransitive), from Old French finiss-, present participle stem of fenir "stop, finish, come to an end; die" (13c.), from Latin finire "to limit, set bounds; put an end to; come to an end," from finis "that which divides, a boundary, border," figuratively "a limit, an end, close, conclusion; an extremity, highest point; greatest degree," which is of unknown origin, perhaps related to figere "to fasten, fix" (see fix (v.)). Meaning "to kill, terminate the existence of" is from 1755.
1779, "that which finishes or gives completion," from finish (v.). Meaning "the end" is from 1790. Finish line attested from 1873.