I think this question may benefit from an answer that goes a little further back to basics than the answers I see so far.
The word aperture literally just means opening. "An aperture" is a phrase that could be used to describe any opening. In the world of photography, though, the word aperture is usually used to refer to a very specific opening inside a camera's lens. What is it an opening in? Well, inside the lens, there are a set of metal "blades", whic overlap each other. The opening, or aperture, can be opened and closed (in a roughly circular configuration - though it may actually be a pentagon or an octagon or other shapes, depending on the construction of the specific lens in question). The way photographers indicate how open or closed the aperture is is with an f-number. Examples might be f/3.5, f/5.6, f/9, or f/11. You may notice I write these all as "eff over" something. The "over" is often left out of speech (one might just say "eff five point six"), but it is quite relevant. The number is actually an expression of the ratio between the focal length of the lens ("f") and the diameter of the opening - so, for example, f/4 on a 100mm lens means that the diameter of the aperture's opening (possibly redundant phrase, but in this case I mean the mechanical blades as the "aperture", which thus does have an opening) is 25mm. At f/8, the opening has a diameter of 12.5mm, etc. This also means that the same f-number on a different focal length lens will have a different opening diameter - while f/8 was 12.5mm for a 100mm lens, that same diameter will be f/4 on a 50mm lens, or f/2 on a 25mm lens.
So, with a zoom lens, you get an interesting thing going on: if you leave the aperture blades in their same physical position, and zoom in or out, this has the effect of changing the f-number, without changing the actual aperture diameter. With many zoom lenses, including yours, the default way of operating is to do this when your aperture is set to be all the way open. Some zoom lenses, especially "fast" and/or high-end ones, have a "constant" maximum (or "wide open", i.e. the all-the-way-open setting of the aperture blades) aperture, which actually does change the aperture diameter as you zoom, even when wide open (even your lens, when set to a non-wide-open aperture like f/8, will change its aperture diameter).
So, on your lens, the listing of f/3.5-f/5.6 is an indication of how wide the aperture is when all the way open. The aperture can still close down from that point, though. You may also find that the minimum (smallest opening, though that's the highest number) aperture also changes as you zoom - perhaps f/22 at the wide end of its range, and f/32 on the telephoto side of things. This would be an indication of the same sort of thing as on the other end, just in reverse - the blades are only able to close to a certain physical diameter, but that diameter yields a different f-number depending on the focal length of the lens.
I hope this all makes sense - I wrote it in small chunks over several hours from my mobile device. If anyone has any questions, I'll try to re-visit it and clean things up. :)
Edit (much later): I think there's actually more going on here than I was aware of when I wrote this answer (in particular: apparent aperture size as well as actual aperture size). I still don't fully understand the details, so I won't try to "correct" this answer (I think it's still mostly a reasonable answer to this question, as asked), I'll merely point out that this may be less than complete and/or, potentially, have portions that are misleading and/or false. (If so, I apologize!) More information is also available in (answers to) another question, so, readers are encouraged to look there, as well.