The most fundamental idea of a detonation engine is that, if you substitute fuel "burning" process with subsonic propagation used in every conventional engines with fuel "explosion" process with supersonic wavefront, the reactions will become more instantaneous and energetic and that improves efficiency. This is the detonation part of detonation engine concept.

The rotating part is a solution to the problem that forcing a continuous sustained explosion inside an engine can be complicated. By letting the explosion constantly happening, expanding, and traveling radially across a thin cylindrical gap, it solves such problems as sustained combus-^H^H^H detonation, fuel supply, etc. It's not the only possible type of an engine based on detonation principle, but so far the most promising. Detonating piston engines for cars, for example, are much less promising.

Engine part is just regular reaction rocket. It shoots the gas out the back. The faster and heavier the gas, the more reaction force it creates.

This isn't the first RDE ever to have been built, fired, or fired in a freefall, but it's finicky and experimental enough that it warrants a news story like this.