Wireless charging is a type of inductive charging, which works via an application of Faraday's Law. Essentially, if a magnetic field changes inside of a wire loop, it will induce a current in that loop. So, wireless chargers producing a time varying magnetic field, and the phone has a wire loop, so a current is induced, which is used to charge the battery.

Why isn't is used much outside of small, personal electronics? 1.) it's not super efficient. Only the energy that goes into producing the magnetic field that goes through the loops actually goes into creating power, the rest is wasted. 2.) It produces quite a bit of heat for how much power it makes. Make enough power to power something big, and it's going to get real hot.