Psychological myths present one with a journey from the known to the unknown which, according to both Carl Jung and Joseph Campbell, represents a psychological need to balance the external world with one's internal consciousness of it. However that may be, the story of the myth itself usually involves a hero or heroine on a journey in which they discover their true identity or fate and, in so doing, resolve a crisis while also providing an audience with some important cultural value.
Probably the best-known classical myth of this type is that of Oedipus the prince who, seeking to avoid the prediction that he would grow up to kill his father, leaves his life behind to travel to another region where he unknowingly winds up killing the man who was his actual father who had abandoned him at birth in an attempt to circumvent that same prediction.
The Oedipus tale would have impressed on an ancient Greek audience the futility in trying to escape or change one's fate as decreed by the gods and would have inspired fear and awe of those gods in the people, thus instilling a desirable cultural value. On a personal level, the story could also encourage a hearer to accept whatever trials he or she was enduring at the time since even a royal personage like Oedipus suffered and, further, whatever one was dealing with was probably not as bad as killing one's father and inadvertently marrying one's mother.