I don't claim to exactly understand how all this works but the range of aperture on a zoom lens works as follows...
The 'f' number is calculated as the focal length of the lens divided by the diameter of the aperture opening. This gives us the following formulae, where f = focal length of the lens, D = diameter of the aperture, and N = the 'f stop' number.
N = f/D
D = f/N
So on the 18-55mm f3.5-f5.6 lens this gives you the following:
At 18mm
D = 18 / 3.5 = 5.1mm
At 55mm
D = 55 / 5.6 = 9.9mm
The bit that I don't understand is why a lens doesn't have the same maximum aperture diameter (D) throughout its range but that probably has to do with the mechanics of how the lens is built and operates - maybe someone else can enlighten us on that bit.
This also explains why you get less depth of field the longer the focal length of a lens - the aperture diameter required to achieve the same f-stop gets larger and larger the further out you go. It also explains why some lenses are bigger than others. For example a f/2.8 300mm lens would need an aperture diameter of almost 11cm
Of course it is possible I have completely misunderstood all of this, it has been a long while since I studied optics, so if someone wants to come along and correct me then please do so!
Put simply, if you want a really blurred background use a wide aperture and a long focal length for a really large aperture diameter and minimum depth of field. If you want really sharp pictures with lots of depth of field use a short focal length and a small aperture for a really small diameter.
An 18mm lens at f/22 has an aperture diameter of 0.8mm!
Hope this helps. (And that I haven't got too many of the details wrong.)
Niall