A misleading headline is making people think that a physical object has been teleported from the ground into space, leading to all kinds of excitement and speculation about Star Trek style teleporters.
In fact nothing like that has happened at all, if you actually listen to the BBC piece, you'll find that what has been transmitted is just information. Nothing physical has moved from the ground into space.
There's a similarly misleading story from MIT's Technology Review.
The sub-headline is somewhat less misleading as a photon (a "particle" of light) is not exactly an object. But even here the photon itself (one of an entangled pair of photons) did not magically jump from the ground into space. In fact it traveled there in the normal way by shining a laser up through the atmosphere to a receiver on the satellite or shining a laser from the satellite down to Earth.
There's a much better explanation at Science Magazine:
The confusion here comes down to terminology, as described in Wikipedia
The reason the satellite "teleportation" is so interesting is that once the quantum information is in space it can be transmitted to other ground stations, or other satellite much more effectively with lasers due to the lack of atmosphere. This allows the creation of a large scale quantum communication network.
What this experiment is really about is secure communication. In particular it can be used as a way for the military to transmit information in a way that would be impossible to intercept (unlike current radio transmissions). This makes it very useful to the military, and explains why the Chinese are doing so much work on it.
It's not a Star Trek teleporter though, sorry.