Current processors use a series of very very small electrical "switches" to dictate one of two possible states: closed or open, or in computer speak, a 1 or 0. The computer collects these various 1s and 0s puts them in order and interprets them. This basic raw computer language is called binary and is the driving process behind all computer functions. So the more switches in a processor, the more powerful it is.
So why is the next processor going to be so much more powerful? Well just recently scientists have figured out how to make the transition from tiny wires to using single photons and atoms. That's right scientists have figured out how to use atoms to alter the state of a photon and vise-versa. So instead of nano meter sized switches we will have switches the size of an atom. Crazy.