If you recite your story a second time, you retell it. After they hear about how you actually slipped on a banana peel, your laughing friends may beg you to retell the incident over and over again.
To retell is to reiterate something, or to tell it again. You might retell your favorite joke every time you have a new audience, or you may find yourself having to retell the details of a fender bender you witnessed once the police show up. When a writer takes up an old theme or story to put their own new twist on it, they retell it: "My goal was to retell the classic Cinderella tale in a modern way."