An analogy used in Plato's Republic. The character of Socrates has been continuing a dialog with interlocutors such as Glaucon in the Republic. Republic is divided into ten "Books" and the Myth of Er is mentioned at the end of the last one.

Essentially, Greek mythology of the day was the basis of religious beliefs of the time, but it was very often self-contradictory: humans were supposed to obey the gods, but at the same time the Greek gods were killing at will, sleeping with men's wives, etc. There was a general message in the religion surrounding Plato at the time of "do as the gods say, not as they do".

Plato seems to have been trying to introduce the concept that morally good people should be rewarded after death, and morally bad people should be punished after death.

Within the dialogue Socrates introduces it by telling the interlocutors the "Myth of Er". In this story, a man named Er dies and sees the judgment of the dead, and the reward of the morally good after a 1,000 year journey, and at the same time punishment of the bad. Er is returned to life, to report what he has seen.

Comparing something to a "Myth of Er" is saying that it began a new series of thought or action where there was none before, and all others can be traced back to it.