Aperture is a bit of a misnomer; a hold-over from simpler times and simpler lens designs. What matters is the entrance pupil, or the apparent size of the aperture as viewed through the front (business end) of the lens. With a simple lens design (a double-Gauss or Tessar, for instance), the physical aperture and the entrance pupil are approximately the same size, but with more complex designs they may bear very little relationship to one another.
The same physical aperture (that is, the iris blades are kept in the same position) can appear to be different sizes at different focal lengths when viewed through the front of the lens. Even with a typical consumer zoom lens, such as an 18-55mm f/3.5-5.6 kit lens, the available f-stops don't correspond to a constant-sized entrance pupil — a simple lens with an 18mm focal length at f/3.5 requires a 5.14mm hole, while a 55mm lens at f/5.6 needs a 9.82mm hole.
The difference between actual aperture (the width of the blades at the diaphragm) and the entrance pupil is a result of magnification by the lens elements between the front of the lens and the physical diaphragm.
Depending on how the zoom is implemented — how the various lens groups are moved in relation to one another — a given iris size can produce an entrance pupil that remains a constant fraction of the current focal length of the lens regardless of the focal length setting. And if the lens is an internal focus design, it can be made to remain at a constant effective f-stop at all focal distances as well. (In a simpler classical design, the effective aperture decreases as you focus closer.)