The idea of using quantum entanglement to 'teleport' a chunk of information is not new. The basic idea is to first take a pair of entangled particles. Entangled particles interact with each other instantaneously over huge distances; if you excite one of them, the other will immediately become excited as well. By using two of these, it is possible to 'teleport' a tiny amount of information. The technique has been shown to work, and has been demonstrated several times. Now, Chinese researchers have broken a record for teleportation: about 100km.
Full story here.
To be fair, the actual photon in question is not moving. Instead, its information is copied and transferred to another photon, which becomes the identical twin of the first. Since the two particles are indistinguishable, it is as though the original particle has moved.
It's hard to imagine how a photon could travel from point A to point B instantaneously, without crossing the intervening space. The idea that information only is transferred is easier to grasp.
However, information is every bit as 'real' as anything else. Quantum mechanics has shown us that information is the building block of the universe (the fact that information is in a constant state of flux in the quantum world is just confusing). You are nothing more than a pile of information, compiling the total data on how many subatomic particles are in your body, their position, energy state, and a host of other factors. If this information were suddenly lost, you would cease to exist (however, it now appears there may be a sort of 'conservation of information' law, where information cannot be created or destroyed, only changed. Therefore, the information stored in your body might exist forever. Immortality, of a sort. But I digress).
Knowing that information is an actual 'thing' of some kind, it's hard to imagine how it can travel without moving. Somehow it seems to do so anyway. The field of quantum communication will undoubtedly be one of the most exciting of our time.