I own a Canon S95, and am considering getting a newer model (e.g. Canon S110 or S120), and I'm comparing the specs. According to DPReview.com, the S95 has a maximum aperture of F2.0-F4.9, and the S110 has a maximum aperture of F2.0-F5.9. However, I know from using my S95 that I can get an aperture range of F2.0-F8.0. What is the story here? What's the difference between 'maximum aperture' and the aperture I can actually get? I would presume that if there were a maximum aperture, it would be a single number, e.g. maximum F2.0 or F1.4 for a much nicer lens. Why is there a range for the maximum aperture? And how can I effectively compare the specifications for the cameras?
The lower the number after the F, the more light gets into the camera. More light means - you can get away with shorter exposure times. - you have lower depth-of-field (which is a good thing in portrait shots)
The ranges given for the lenses are the values for the wide angle and the tele setting of the lens.
Generally you want the numbers to be as low as possible, because this is the MAXIMUM aperture. You can close the aperture to something like F/22 or F/30 with all the lenses.
Remember: the reason why bigger numbers mean less aperture is that this really is a ratio. F divided by 2.0 or something.
On a zoom lens, it's common for maximum aperture to vary from one end of the zoom range to the other. Typically, the largest aperture (smallest f-stop number) will be available at the wide end of the zoom range, and it will decrease throughout the range until it reaches the smallest maximum value (yes, it's sort of confusing) at the telephoto end of the zoom ranges.
In your example, the f/8 end of the aperture range is achieved by stopping down the lens -- this value can also vary through the zoom range, but it's less common, and typically isn't as closely scrutinized since people tend to be more interested in wide apertures for letting in lots of light.
Although your example deals with a lens that's fixed to the camera, this variance of maximum aperture across the zoom range happens with interchangeable lenses, too. One of the hallmarks of higher-end zooms, in fact, is a "fixed maximum aperture", which you'll see expressed with a single f-stop value.
 As a final note, prime lenses (lenses that don't zoom), have a single value for maximum aperture intrinsically, because the lens has only one focal length.
The aperture (the hole inside the lens through which the light passes) can be made very small, but has a limit to how big it can get. The f/ number range given with a camera is the range for furthest open that the lens can get. It is given as a range because when the lens is wide (at short focal lengths) the f/number is smaller than when the lens is zoomed in (long focal lengths).
An f/2 - 5.9 lens does not mean that you can only put the aperture to f/5.9, but rather than when you are at the widest point, you can open the lens to f/2, but when you are zoomed all the way in you can only open it up to f/5.9.