The inductive thing is simple. Think of it as a transformer that you can take apart, because that's what it is. One set of winding in the base, a piece of metal sticking up (usually), and another set of windings in the gizmo to be charged.
A changing electrical current through a wire creates a changing magnetic field, and vice-versa. You couple the magnetic fields, and you transfer electrical power from one place to another. It's a physics thing. You can change the frequency of the field, and the shape of the field, but you need the same amount of magnetic energy as electrical energy...also a physics thing.
You can also transmit electrical energy electrostatically, which would be having a capacitor that you could take apart.
Either way, a neat thing.