Polybus was King of Corinth who ruled along with his wife Merope. He was the foster father of Oedipus, when he received him as a baby from a shepherd. As he and Merope did not have children, they agreed to take Oedipus into their home and care for him.
When Oedipus hears word of the Delphic oracle's prophecy that he would kill his father, Oedipus determined not to fulfill it. He left Corinth forever, unknowing that Polybus was not his actual father. Later, Polybus dies of an unknown cause, and this fills Oedipus with elation, believing he wouldn't have to kill his father after all.