Most people have never heard of Marin Soljačić.  He is a physicist of Croatian descent at M.I.T. who, along with his team, invented wireless non-radiative energy transfer.  Essentially, to a layman such as you and I, wireless power.  For his work, he was awarded a MacArthur Fellowship.

Approximately one hundred years ago, Nicola Tesla begins theorizing that wireless power is achieveable.  It was his idea to transmit electricity wirelessly over long distances, as the concept of the power grid had not yet been conceived.  He even went so far as to build a 100 ft. tower in New York, the Wardenclyffe Tower.  Unfortunately, he was unable to complete his experiments due to monetary issues.

Enter Professor Soljačić.  He would not have pursued his idea if it was not for his wife having a cell phone with a low battery.  It was constantly beeping at night keeping him awake, and during one of those fruitful nights he thought that there has to be away to charge the cell phone without plugging it in.  And so the experiments began.

As for the technology itself, I think it is best explained by Eric Giler.  He is the chief executive at Witricity, the company formed to bring the new technology to the marketplace.