Quantum entanglement works like this: You have 2 particles, let's say photons, which are entangled. When you observe the spin of one of the photons and find that it is +1, then you also know that the spin of the other one must be -1. If instead when you observe it, it turns out to be -1 than in the same way the other one will be +1.
Somehow, the spins of these two photons are intrinsically linked. Linked in such a way that at the very moment (and I mean that literally) that you observe the state of one of the photons, the state of the other photon (no matter where it is in the universe) can be predicted with total accuracy based on the measurement taken from the first.
Now at this point it might seem as if this has all you need for faster than light teleportation: you could build two machines with a bunch of entangled particles between them, send one of them far away, and use the machines to transmit the quantum state of whatever you want to teleport to the other so that the thing can be rebuilt. Sadly this won't work.
The problem lies here:
Until you make the measurement on one of the particles than their states are completely indeterminate (a phenomena that's called quantum superposition). You can't know what will be the photon's spin until you check it. And you can't do anything but measure the particle if you want to keep the entanglement intact. If you force the particle to be in the state you want it to be, than the entanglement will instantly break.
So you're left with a weird situation where you can know exactly what the state of a particle right across the universe is but not be able to use it to transmit information.