Oedipus Rex (or Oedipus the King) is a Greek tragedy written by Sophocles and performed circa 429 BC. The play focuses on the aftermath of a fulfilled prophecy that predicted that Oedipus would kill his father, Laius, and wed his mother, Jocasta. It is understood at the beginning of the play that Oedipus has done just that; in his attempt to avoid his fate (which he had heard from the Oracle of Delphi), Oedipus--who had been abandoned on a mountainside as a child by Laius and adopted by King Polybus and Queen Merope--leaves for Thebes. On the road to his destination, he meets and kills his biological father, and upon reaching Thebes, he wins his mother's hand in marriage by answering the riddle of the Sphinx.
Oedipus Rex begins after these events have occurred but before Oedipus has realized that the prophecy has been fulfilled. The plot follows Oedipus's reign as king and his desperation to end the plague that is destroying Thebes. Because of Oedipus's own stubbornness and refusal to listen to those around him, the truth of the prophecy is eventually revealed; mad with despair, Jocasta kills herself and Oedipus gouges out his own eyes and begs to be exiled.
Thus, the title of Oedipus Rex is significant in that it locates us contextually within the span of Oedipus's story; this play does not deal with the events of Oedipus's childhood, nor with what will transpire after his exile. Rather, we are placed squarely within Oedipus's reign as king. It also places emphasis on the self-fulfilling nature of the prophecy. With his title as "king" intact, Oedipus has clearly managed to fulfill the prophecy. Knowing that this is a tragedy further suggests that we are about to see the consequences of him having done so.
The title Sophocles gives this play indicates several things about its focus and themes.
To start, the myth of Oedipus has several stages, and the audience Sophocles was writing for would have known each stage. The title signals to the audience which portions of the myth the play will cover.
Since Sophocles was working in a known, if fairly new structure (tragedy), his audience is likely to have known that the title indicates that play will cover not a period in which Oedipus is successful as being a king, but that he'll fall from this position.
They can know to look for a tragic flaw, and for Oedipus to fall because of it.
Finally, because of the way the king relates to his people in this period, the title signals that the play will carry implications for the entire community. It isn't just a private matter: it will have public or communal implications.