The Canterbury Tales is a fantastic example of a framed story. The larger tale is that of a diverse group of pilgrims gathering at the Tabard Inn preparing to travel to Canterbury Cathedral. Chaucer doesn't spend much time on the travel conditions, but instead entertains the reader by creating smaller stories told by the various characters. A contest is announced that the best storyteller will receive a free meal once the pilgrims return from their journey. All of the contest entries (the Miller's Tale, the Knight's Tale, etc.) are the stories within the larger story of the pilgrimage.
Well, the Canterbury Tales is actually many stories within stories. First you have the introduction of the "main" story, which is the narrator going on a pilgrimage with a bunch of different types of people (most of whom he describes in the prologue). While that story is taking place (the walking, the talking, the decision of who gets to talk when and why) there are many little stories within the main story. The "main story" frames all of the little tales that the pilgrims tell. Those stories take on their lives since the chapters are divided into "The Knights tale" etc... One could read the tales individually, or in the context of all of the tales, and that's what makes it stories within a story. One could even say, that the real story, is the rich, intricate tapestry of medieval social life, combining elements of all classes, from nobles to workers, from priests and nuns to drunkards and thieves.