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Since King Laius was not killed in a battle or a war and did not die in a manner that befitted a king, his city Thebes is cursed with a disease by the Sphinx, the Greek demon of destruction and bad luck. Additionally, for anybody to enter or leave the city, they had to correctly answer the riddle of the Sphinx, failing which they would then be strangled and killed. Therefore, when Oedipus reached the gates of Thebes, the Sphinx posed him with this riddle.
What is that, which in the morning goeth upon four feet, upon two feet in the afternoon and in the evening upon three?
Oedipus figures out the answer to the riddle – Man; as he crawls when he is a baby, walks on his own feet as an adult and needs the help of a walking stick, a third leg, as he grows older. Impressed with his ability to quickly think, the Sphinx accepts defeat, allows him to enter Thebes, and also makes him the ruler of the city by virtue of having freed it from the curse. He also goes on to marry the dead widow of the king, Jocasta, his own mother.
After some time, with the intention of investigating who killed the King Laius to lift the curse on the city, Oedipus goes on to discover that it was he who had killed him, and also found out that by doing so, he had killed his own father and consequently gone on to marry his own mother.
Overcome by guilt and shame at what had happened, Jocasta hanged herself, and a grief struck Oedipus took two of her dress pins and blinded himself. He was then driven into exile where he finally died after years of wandering.
The above legend has been told and retold in many versions and also forms the basis for a psychological condition called The Oedipus Complex made popular by Sigmund Freud.
Freud used the name to describe a childhood neuroses where a male child has an unconscious desire for the love of his mother which also includes jealousy towards the father. In simpler terms, the son feels so protective of his mother and her love towards him that he cannot even tolerate his father being close to his mother.
The underlying theme that Freud uses here is the fact that there inherently exists a conflict between the younger generation (Oedipus) and the older generation (Laius) and the incident at the Cleft Way just goes on to highlight the insistence of both generations to stick to their points of view and an unwillingness to let the other generation win at any cost. What follows consequently is a violent struggle between generations where the younger one wins.
But in the process, the wisdom of the past is lost, Oedipus pays no heed to what Laius has to say or what his point of view is. He is only interested in sticking to his point of view and ignores everything else.