The Mystery of the 3rd Floor Corridor

Having grown up with the children of death eaters, Alistar Morningstar knew very well that his first year of Hogwarts was going to be very interesting. That of course was before they discovered a trapdoor on the 3rd floor, guarded by a fierce three-headed dog. What's under the trapdoor? Why does the DADA teacher want it? And why the hell did Hagrid name the dog "Fluffy"?