A retelling is a new version of an old story. Somehow, your retelling of your dad's hilarious tale of catching a shoe instead of a fish is never quite as funny as his version.
Retelling comes from the verb retell, or "tell again." You can use this word for literal retellings, when an anecdote is simply told all over again for the second (or third) time. It's also useful for updated versions of classic stories. The movie Clueless is a retelling of the Jane Austen novel Emma. And Jane Smiley's A Thousand Acres is a retelling of Shakespeare's King Lear.