The number is calculated by this formula: (focal length)/(Diameter of the entrance hole). Usually a long lens has a long focal length - it is very roughly the distance between the end of the lens and the sensor. The "entrance hole" is the hole in the aperture mechanism.

In the diagram above, the f-stop number is f/2, as the focal length is twice the Diameter of the entrance pupil.

In the diagram above, the f-stop number is f/4, as the focal length is four times the diameter of the entrance pupil. The value is higher, as the aperture is smaller.

In this last aperture diagram, the f-stop number is also f/4. This time, it is not the entrance hole that is smaller, but the focal length that is bigger than in the first diagram. (Click on the diagrams to display them in real size, if you do not believe me.)
If you change from f/2 to f/4 on your camera, you will cut the diameter by half, and consequently you cut the amount of light by four.

In other words, if you have a situation where you have set the camera aperture to f/2 and the shutter speed to 1/400 of a second, and you then change the aperture to f/4, you can keep the same amount of light by slowing the shutter speed down to 1/100 of a second.
So why is it called stop? It seems to be mostly old habit. The aperture hole, the entrance hole or "entrance pupil" as it is also called, "stops" light from getting in to the camera.
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