Teleportation is the movement of objects from one place to another, more or less instantaneously, either by paranormal means or through technological artifice. The concept has been widely used in science fiction.
Teleportation involves dematerializing an object at one point, and sending the details of that object's precise atomic configuration to another location, where it will be reconstructed. What this means is that time and space could be eliminated from travel -- we could be transported to any location instantly, without actually crossing a physical distance.
Quantum teleportation, or entanglement-assisted teleportation, is a technique used to transfer information on a quantum level, usually from one particle (or series of particles) to another particle (or series of particles) in another location via quantum entanglement.
The difference with quantum teleportation is that you have copies. It does not transport energy or matter, nor does it allow communication of information at superluminal (faster than light) speed. Its distinguishing feature is that it can transmit the information present in a quantum superposition, useful for quantum communication and computation.
A teleportation machine would be like a fax machine, except that it would work on 3-dimensional objects as well as documents, it would produce an exact copy rather than an approximate facsimile, and it would destroy the original in the process of scanning it.
A few science fiction writers consider teleporters that preserve the original, and the plot gets complicated when the original and teleported versions of the same person meet; but the more common kind of teleporter destroys the original, functioning as a super transportation device, not as a perfect replicator of souls and bodies.