Laius and Jocasta just foudn out that their son, Oedipus would grow up to kill his father and wed with his mother.
Oedipus was given to a herdsman in a far of kingdom so he would be seperate from his parents.
Oedipus found out about the prophecy and decided to travel to a far away land called Thebes to get away from his "mom and dad".
On his way to this new kingdom, he came along path with a carriage and he killed the driver and the passenger. Little did he know, he had just kill his father, King Laius.
The sphinx, who was a body of a lion, wings of an eagle, and head of a women had been sent to Thebes from the gods to punish the king for raping a prince.
The only way to get past the sphinx is by answering her riddle, if you answered incorrectly she would eat them. When Oedipus came to the sphinx, he was able to solve the riddle and the sphinx killed itself.