The number in the f stop spec is a ratio of how many times the maximum effective aperture goes into the focal length.
For example, if a 50mm lens has a maximum aperture of f1.8, then we can divide 5o by 1.8 and get 27.8. This tells us that the diameter of the effective aperture in this lens is 27.8 mm.
If the diameter was f5, then the diameter of the aperture is smaller, only 10mm. You can see how higher f stop numbers result in the diameter of the aperture being smaller.
This also means that the actual diameter for a particular f stop can change depending on the focal length of the lens. As the lens gets wider, it can gather more light, because it covers a greater field of view (there's more it can see that is reflecting light). So to make sure that it isn't overwhelmed with light, the diameter of the aperture is reduced (f5 on a 50mm lens has a diameter of 10 mm, but on a 10mm lens the diameter is only 2mm.)
In fact, the lens itself will tell you how to calculate this. You see the aperture settings displayed as f/8, or f/5.6. The F actually refers to the Focal length, so f/5.6 is telling you that if you divide the focal length by 5.6 you'll get the diameter of the aperture.