The Movie: Photon torpedoes are fueled by the explosive hatred that matter and antimatter have for each other. They are a staple in most Star Trek incarnations, and are a great way to get around the fact that most Earth-based weaponry wouldn't work in space — for example TNT, dynamite, and gunpowder require oxygen to work, but antimatter reactions occur on the quantum scale, and can theoretically work in any environment.
Real Life: Kudos to Star Trek for trying to skirt the "redox" problem. But would a photon torpedo work in real life? From what we know, nope. The big problem is that antimatter is really, really rare. For whatever reason, in the early universe, matter won out against it, which is awesome for us because we are all on Team Matter. There are occasionally patches of the universe that appear to be rich in antimatter, such as the Milky Way's galactic center, but those are exceptions. Of course, we can also produce antimatter artificially in places like CERN, but it is literally the most expensive material in the world to create. Ever. It costs $25 billion to produce a single gram. Unless you've got that kind of money lying around, photon torpedos will remain fictional.