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
At 1/2000th both a running cheetah and a running squirrel are completely frozen. I haven’t yet found anything that isn’t frozen with that setting. I suspect at that point you’re in the domain of bullets, very outstretched springs and the like.
Stabilization doesn't help with subject movement, it only helps with the camera's shake.
So with this level of stabilization, you'll take a picture of a running cheetah at 1/25 as if it were 1/2000 only as far as the stability of the camera is concerned. So if you're not tracking the cheetah you'll get a sharp background because the shaking of your hands has been nullified, but the cheetah is still moving within the frame and still blurry.
However, it's not the aperture range that matters. Theoretically, if earth were not rotating, then 10 stops would still be useful for long-exposure photography. In other words, the stop differences in stabilization are more useful when you think of then in terms of shutter speed, NOT aperture.
