I just took a quick look at the video, and I can see that the guy doesn't get into the definition of what an f-number actually is (which is understandable for a beginners guide)
Mathematically, an f-number is the ratio of the focal length of the lens to the diameter of the aperture (as it appears when seen through the front of the lens). If a lens has a focal length of 50mm and an aperture of 25mm, the f-number is 50/25 = 2. The convention is to say it's an f/2 lens because for exposure purposes we don't need to know that the aperture is 25mm and that the focal length is 50mm, we just need to know the ratio of those two numbers.
If we take that same lens and "stop down" two clicks on the aperture ring to f/4, what we're physically doing is reducing the aperture to 12.5mm, because 50/4 = 12.5. But we don't care that it's a now a 12.5mm hole, we just care that the exposure is now two stops less than when we started - and that's a meaningful number because each stop is a halving of exposure, so we've now got a quarter of the orginal exposure.
-R