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As jolepp said, f-stops are fractions, the ratio of the iris diameter to the focal length. So a 50mm lens with a 12.5mm aperture is 12.5/50 or 1:4 or f/4.0. We use the notation f/nn instead of 1:nn because of 1) tradition and 2) laziness.
On zoom lenses with variable maximum apertures, we see a notation like 18-55/3.5-5.6 or 1:3.5-5.6 18-55mm. This means the maximum aperture at 18mm is f/3.5 and the maximum at 55mm is f/5.6. When we stop those way down, the LCD screen on the camera reveals different minimum apertures. On the DA18-55 it's f/22 at 18mm, and f/40 at 55mm.
We use these f/numbers just so we don't have to worry about the actual iris diameters, only their relationships. We can easily control DOF while maintaining the same exposure by varying the f-stop and shutter speed in sync -- open the aperture by on stop whilst doubling the shutter speed, or close the aperture one stop and halve the speed. Same amount of light, different optical effects.
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