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.
"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.