Quantum teleportation is a way of transferring the quantum state of one quantum system to another using the quantum entanglement between two other systems.
For example, let's assume Alice and Bob share an entangled pair of particles A and B, and Alice wants to teleport the information of another "message" particle M to Bob.
What Alice does is interact her half of the entangled pair, A, she shares with Bob, so that now the message particle M is entangled with Alice's other particle A.
Next Alice measures both of her particles A and M and tells what the outcomes of these measurements are to Bob. Because the message particle M was entangled with Alice's other particle A, and Bob has the information of Alice's measurements, he can use this information to recreate the original message particle M out of the one he has B.
What makes quantum teleportation special is that we didn't need to physically move the message particle M from Alice to Bob.