by 1862, in sporting jargon (curling), "to play (a match) again," from re- "again" + play (v.). Of sound recordings (later video, etc.), "reproduce what has been recorded," by 1912. Related: Replayed; replaying.
The noun is from 1895 as "a replayed match" in sports. The meaning "action of replaying" a sound recording, film, later also video, etc., is by 1953.
name of the boy-hero in J.M. Barrie's play "Peter Pan, or The Boy Who Wouldn't Grow Up" (1904), first introduced in Barrie's "The Little White Bird" (1902). Used allusively for an immature adult man from 1914 (by G.B. Shaw, in reference to the Kaiser).
Well, Peter Pan got out by the window, which had no bars. Standing on the ledge he could see trees far away, which were doubtless the Kensington Gardens, and the moment he saw them he entirely forgot that he was now a little boy in a nightgown, and away he flew, right over the houses to the Gardens. It is wonderful that he could fly without wings, but the place itched tremendously, and, perhaps we could all fly if we were as dead-confident-sure of our capacity to do it as was bold Peter Pan that evening. [Barrie, "The Little White Bird"]
1939, "of or pertaining to desire felt for the opposite-sex parent," from Oedipus complex (1910), coined by Freud from Sophocles' play "Oedipus Tyrannus," in which the title character, the Theban hero, answers the Sphinx's riddle and unknowingly kills his father and marries his mother; from Greek Oidipous (see Oedipus). The name was used figuratively in English from 1550s for "one who is clever at guessing riddles," which had adjectival form Oedipean (1620s).