The Hero of Kvatch starts out as an ordinary prisoner who is locked up for reasons that are never disclosed. In progression through the main story line of Oblivion, the hero will be asked to save Martin Septim, the Heir to the thrown of Cyrodil. He is found in the city of Kvatch and wont leave until the Oblivion Gate which is outside the city is closed. After the gate is closed the character is bestowed the title of Hero of Kvatch. Through the rest of the game many of the npcs will refer to the character as hero or savior of Kvatch.
The New Sheogorath
It is heavily implied that the Hero of Kvatch is Sheogorath in The Elder Scrolls V: Skyrim. At the end of the Shivering Isles you replace Sheogorath as the new Prince of Madness. During the conversation between Sheogorath and Pelagius the Mad in Skyrim he says, "You are the best Septim that's ever ruled. Well, except for that Martin fellow, but he turned into a dragon god, and that's hardly sporting... You know, I was there for that whole sordid affair. Marvelous times! Butterflies, blood, a Fox and severed head... Oh, and the cheese! To die for."
The events he is referring to are major events the player can take part in from Oblivion. Martin turning into a dragon god is from the end of the main story, the fox refers to the Gray Fox from the Thieves Guild and the severed head refers to the story in the Dark Brotherhood.