Homer's Odyssey contains a number of stories that appear within the larger framework of this epic poem.
Early in Odyssey 1, when Zeus and Athena are discussing Odysseus' situation, they also recall the story of Agamemnon, his return home after the Trojan War, and how Agamemnon was killed by Aegisthus. This story prepares us for the challenges that Odysseus himself will face when he returns home from Troy.
The Odyssey also contains within it the story of Telemachus' adventures. The first four books of the Odyssey are sometimes called the Telemachia, because they relate the adventures of Telemachus as he searches for his father. Telemachus' adventures also frame other stories, such as the one that Menelaus tells Telemachus about the time he spent in Egypt.
Finally, of course, the Odyssey as a whole serves as the frame for the adventures of Odysseus himself. In Odyssey 9-12, Odysseus tells the people of Phaeacia about the trials and tribulations he himself faced after he left Troy.