A stop generally is a doubling/halving of light intensity at the sensor. For apertures this means a factor of sqrt(2) on the diameter (because the area is what matters), for exposure times a doubling/halving of the time.

"Stops of stabilization" in this specific context refers to a standardized CIPA test which determines a shutter speed where the image remains acceptably sharp. They then calculate the number of stops to 1/focal-length, which is a rule of thumb for getting sharp images from the 1950s. So if a 200mm lens produced a sharp image at 1/10s in the CIPA test, then that would be 1/10 -> 1/20 -> 1/40 -> 1/80 -> 1/160 -> 1/200 about 4.3 "stops of stabilization".

The results from the CIPA test don't really hold up to the real world though once you move beyond ~4 stops.

it's an abstraction of the aperture size and exposition time. If you expose twice as long it gives the same light than an aperture twice the surface. Those 2 are discrete in camera, so it is abstracted as stops. Exposure time is limited by movement, and aperture size is limited by the optics itself. Sensor stabilization allows to gain "stops" by extending the exposition time before the image becoming blurry from the photographer movement, thus allowing as much more light to come