We know E=mc^2 (mass and energy are equivalent).
We know that rockets move by ejecting mass at high speed in a direction counter to the desired direction of movement. The rocket shifts forward an equivalent amount (m1v1=m2v2).
We know that it is possible to focus EM radiation emissions.
So far so good.
The "magic" here (used in the sense of sufficiently advanced tech, of course), is that the EM emission is entirely unidirectional.
So instead of throwing mass out the nozzle, we're throwing energy. And since E=mc^2, we get the same effect: RmRv=E/c (rocket mass times rocket speed equals Energy over c (since m2v2 = (E/c^2)c).
Very, very, very cool.