Teleportation is one of the strangest things to pop out of quantum mechanics. Two parties, typically named Alice and Bob, each share one member of an entangled pair of particles. Bob travels off to some distant location, and Alice decides she wants to send him a message. Actually Alice wants to send him another particle she has in her possession. She can do this using teleportation.
By doing a series of prescribed measurements and then telling Bob what the mesurement results were, this can be pulled off. Depending on the measurement results Alice got Bob applies a "unitary transformation" (which can be a magnetic field applied in a specific direction say) to his member of the entangled pair of particles. Strangely, his member of the pair ends up in the same state as the particle Alice wanted to send him.
So teleportation isn't really about physically making a particle disappear at one location and reappear somewhere else, its about transmitting the information about that particle. But this really isn't all that different because microscopic particles are all identical, except for their states at a given instant. One electron is the same as any other. So, if Alice in Los Angeles has an electron in her possession in some state and is able to use teleportation to essentially map that state onto an electron that Bob has in New York, Alice has in effect sent Bob her electron.
This raises an interesting question-are you as a person a thing that is a collection of "stuff", or are you an assemblage of information? Would it be you that popped out in New York if we could transmit the states of every particle in your body from Los Angeles to a similar collection of particles in New York or would it be a duplicate? Right now this is just a philosophical question, such a feat may forever be beyond the limits of technology. Researchers have so far teleported just a single photon about a mile and a half. While this doesn't sound like its useful for teleporting say Captain Kirk it does have applications in communications.
Anyway, the movie is called Jumper. You can read about it on the New York Times at: