The three-headed dog guarding the Philosopher's Stone is named Fluffy. Hagrid leaves Fluffy guarding a trapdoor at Hogwarts as part of the magical protections placed around the Stone.
Harry, Ron and Hermione encounter Fluffy during their first year. Hagrid explains that the enormous dog belongs to him, and the trio discovers that music can lull Fluffy to sleep. This clue later helps them get past the creature when they descend through the trapdoor.
Fluffy is one of several obstacles protecting the Philosopher's Stone, alongside Devil's Snare, flying keys, a giant chessboard and a logic puzzle involving potions. The protections were arranged by Hogwarts staff to prevent anyone from reaching the Stone, which can be used to create the Elixir of Life.
Fluffy is often confused with other famous animals in the series. Aragog is a giant spider, Norbert is a dragon that Hagrid raises briefly, and Fang is Hagrid's large but ordinary boarhound. None of those creatures has three heads or guards the Stone.