Greek tragedy's central characteristic is following a noble character who experiences a change in fortunes due to a fatal flaw. This character is essentially good at heart, but their fatal flaw is what causes their misfortune. This misfortune and the character's reaction to it is what creates the tragedy.
In Oedipus Rex, Oedipus is the tragic hero. He is shown to be a good man and a good king. He cares enough about his parents (or who he thinks are his parents) that he leaves home when hears the prophecy that he will kill his father and marry his mother. He loves his wife and children, and he is concerned about the welfare of his people.
His reversal in fortune occurs when he learns the truth about his parentage and his marriage. His fatal flaw is his own anger, which is pointed out by Tiresias. Had he not let anger get the better of him, he would not have unwittingly killed his own father, who offended him while Oedipus was traveling all those years ago.
(Some have offered different interpretations of what Oedipus's fatal flaw might be. Some claim that it is his pride in fighting against his fate that brings him down. Others claim that it is his arrogance—in assuming he can handle the truth behind what is causing the plague in his kingdom and his insistence in pursuing this truth—that brings him low.)
Greek tragedy also seeks to arouse pity and terror in the audience. This certainly happens in Oedipus Rex. The accidental incest between mother and son is horrific enough, but Jocasta and Oedipus's violent reactions to this terrible truth arouse even more horror. The audience feels pity for the both of them, since Oedipus and Jocasta are not bad people—both are noble rulers and affectionate people: to see them suffer as they do creates great sympathy in the audience.