The oracle at Delphi tells the King and Queen of Thebes, Laius and Jocasta, that their infant son will kill them. So, they pinion his feet and tell a shepherd to take him to the mountains to die.
The shepherd takes pity on the baby, and he gives him to another shepherd from the nearby city-state Corinth. There, the King and Queen, who could not otherwise conceive a child, welcome the boy as their own.
Once a teenager, Oedipus (whose name means "swollen foot") is told by a peer that he is a bastard, something he has been paranoid about for a while. To confirm this, he visits the Oracle at Delphi, which tells him he will kill his father.
Thinking his father is in Corinth, he runs as far away from that city-state as he can. On the way to Thebes, he meets a man driving a cart of slaves at a crossroads. The man deals harshly with the teen, who is crippled and walks with a cane. The man tells him to move from the road. Oedipus refuses, and the two come to blows. Oedipus strikes him dead with his cane.
As he enters the city of Thebes, he answers the Riddle of the Sphinx and frees the city from the plague. Joyful, they crown him their King, a position that has been vacant. Oedipus must marry the sitting Queen, Jocasta.
Little do any of them know that Jocasta is Oedipus' mother and the man he killed at the crossroads is his father. All this is the antecedent action to the play Oedipus Rex.
Oedipus kills Laius, the king of Thebes, at a cross-roads, where Laius wants Oedipus to make room for his passage and Oedipus refuses to oblige. This proves to be an error on the part of Oedipus--'hamartia', to use Aristotle's term--as he unknowingly kills his own father to enter Thebes, becomes the king and marries the Queen--his own mother.
Laius was told that one of his sons would kill him. So when Oedipus was born, the child was handed over to a shepherd to be thrown from the height of a mountain. However, the shepherd took pity on the child, and the baby was later adopted by Polybus and Merope--the king and the queen of Corinth. When young Oedipus visited the Delphic Oracle to know his future, he was told that he would kill his father and marry his mother. Having escaped from Corinth, Oedipus moved on to reach the said cross-roads.
The cross-roads stand for a set of choices and the freedom to exercise one of the choices. Oedipus didn't know Laius; he didn't know that Laius was his real father. He could have stood away to allow Laius go with a cartload of slaves. But he chose to fight and Laius was killed by him. Then, as he entered Thebes and answered the riddle of Sphinx, he was welcomed as the new king of Thebes. Oedipus married the queen, Jocasta, the widow of Laius.
Thus, as a consequence of his error at the cross-roads, both the prophecies of the Delphic Oracle came true.