The f-number is in use to express how much light a lens can capture, so the 85mm f/1.8 and 24mm f/1.8 can capture the same amount. Here, f is the focal length, and f/1.8 means that maximum aperture diameter is 47.2mm in first example and 13.3mm in second.

What you have to consider here is that the 85mm lens has a much narrower field of view, therefore it has to gather the same amount of light from a much smaller area - to compensate the narrow view, aperture has to be bigger.

How much the aperture has to be bigger is linearly correlated to focal length. We could say that a 24mm lens with 13.3mm aperture can gather as much light as a 85mm lens with 47.2mm aperture, but talking about the F-number makes this much easier to notice.

Please note that f-number is purely a result of geometrical calculation, not taking into account any loss of light inside the lens. For most photography needs, that's close enough. When you need to exactly match gathered light levels (such as when combining video footage taken with different lenses), you should be looking at T-number.