A stop is a doubling or halving of the amount of light reaching the sensor, and it's the common unit used to compare exposure changes across aperture, shutter speed and ISO.
A stop is the unit that lets the three exposure controls talk to each other. Because a stop means the same thing wherever it appears, one stop of light lost to a faster shutter can be handed straight back by opening the aperture a stop or raising ISO a stop, and the frame's brightness stays put. Without that shared unit, every exposure change would be guesswork.
Stops also measure things that are not camera settings: a lens might be rated to lose two stops of brightness at the edges of the frame, a neutral density filter is sold as a 6-stop or 10-stop piece of glass, and a modern sensor's dynamic range is quoted around 14 stops. A photographer who thinks in stops can hear 'the shadows are two stops under' and know exactly how far to lift them, instead of dragging a slider back and forth and hoping.
A scene meters correctly at f/4, 1/250s, ISO 200. The photographer wants a blurred-motion look and needs the shutter at 1/15s, which is four stops slower, so four stops of light have to come out somewhere else. Closing the aperture from f/4 to f/16 removes exactly four stops, stepping f/4, f/5.6, f/8, f/11, f/16, and the exposure matches again.
If the lens only stops down to f/11, that is three stops, leaving one stop over, which dropping ISO 200 to ISO 100 takes care of. Every one of those moves is a clean, countable step. Half and third-stop clicks exist on top of that because the eye can still spot about a third of a stop of brightness difference in a print, but rarely less, which is why exposure compensation dials are marked in thirds.
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