What is a weight-shift-control category aircraft?
Basically, it's a powered hang glider.




  Weight-shift control (WSC) aircraft means a powered aircraft with a framed pivoting wing and a fuselage controllable only in pitch and roll by the pilot’s ability to change the aircraft’s center of gravity (CG) with respect to the wing. Flight control of the aircraft depends on the wing’s ability to deform flexibly rather than on the use of control surfaces. 


— FAA H-8083-5 Weight Shift Control Aircraft Flying Handbook

They're commonly called "trikes" and are literally big delta-wing hang gliders with a lot more structure and an engine. Check out a cockpit video of one in flight!