This technology was in fact demonstrated by Nikola Tesla in the late 1890's before the FBI pulled the plug (pardon the pun) on it. Although explained in the video rather nicely, the basics of the technology revolve around the principle of electromagnetic induction - an electric current moving in a closed loop will generate a magnetic field, and vice versa. Hence if two coils are present one inside the other, the second coil can turn the magnetic field back into electricity. This is the basis of transformers. The key to making this work over long distances, however, is to make the respective coils oscillate at the same frequencies and 'couple' so that power can be transferred.
As pointed out in the comments section of the video, there will be some issues around who pays for the power (ie. can anyone tap into it?), but imagine a world where battery powered devices never go dead!
*PowerbyProxi was spun out of the University of Auckland in 2006.