At its most basic, the idea is that you cannot measure a quantum state without altering it. If you wished to know exactly a given quantum state, you would need an infinite number of copies on which to perform an infinite number of measurements.

Now, because of this, if you want to transmit a state, you cannot just measure it, and then use a lab elsewhere to recreate it. You either have to transmit the state physically to the other location (which could be difficult, because quantum states are fragile) or you can perform 'quantum teleportation', in which case you can recreate the state by transmitting only classical information (i.e. the outcome of a measurement). The tricky part is, you already have to share an entangled state* to perform quantum teleportation, but there are ways of doing this. In fact, at a glance, I'm pretty sure that the paper in question was detailing one such way of creating entanglement remotely.

In effect, you successfully transmit a quantum state without either party knowing at any point what the transmitted state is. This could be useful if you want to transmit a state from one part to another part of a quantum computer with which to perform computations, for example. It's all a little complicated to explain so briefly.

*not strictly true, but you need to have some form of quantum correlations, and until recently it was thought that entanglement was necessary.