When Oedipus was born, his parents, the King and Queen of Thebes, learned of a prophecy that their son would kill the King and marry his mother. They gave Oedipus to a shepherd who was ordered to leave the baby to die on a mountain.
Instead of leaving the baby, the shepherd took the baby the childless King and Queen of Corinth, who raised them as their own.
When Oedipus learned of the prophecy, he ran away from Corinth, not knowing that the King and Queen are not his biological parents. Surprisingly, on his journey he got into a fight with a man and killed him, but carried on his way.
Before entering upon Thebes, Oedipus had to face the monster called, Sphinx. To pass you would need to solve her riddle, if not she would get terribly mad and strike. Fortunately, Oedipus was the only man who was able to solve the riddle.
Since the King of Thebes had recently been murdered, making the Queen a widow. Without either knowing that they were mother and son, they married and had children together. Unfortunately, a plague spread through Thebes, and many believed it would only stop if the killer of the King was found.
Eventually, Oedipus had learn he had killed the King, and learned it was he who had killed him, Oedipus had followed the prophecy. Once learning, he told his mother/wife, and she decided to kill herself. Oedipus decided to gouged his eyes out, because he was too blind to see the truth. Oedipus was later exiled.