A wide angle lens gives you a wider view, which is often nice when taking landscapes. Most digital cameras, especially in this point n shoot category, have a panorama mode, which helps you take a series of side by side images. Later on the computer you use a program (provided with the camera) to stich these together into a wider (or taller) image. In ways this is a substitute for a true wide angle, in some ways it is better.
With 35mm film, 'normal' lens length is 45-50 mm, which gives background to foreground proportions that you normally see. 35 mm is mild wide, 25 mm or so is wide or lower is wide.
To judge how wide a digital camera's lens is, you have to adjust the actually range (typically 5.5 - 16mm, for 3x zoom) for the sensor size. Some reviews and product manuals give you a 35mm equivalent.
The numbers I see on dpreview for the A520 are 35mm equivalent at the wide end, 140 mm at the tele end. Looking at other Canon offerings, this appears to be typical. A few get down to 28mm equivalent.
http://www.dpreview.com/reviews/specs/Canon/
For a given zoom range, you are trading off the wide view against the tele view. The S80 has a 28-100mm range. Read the reviews of the S80 and A520, and look at the sample pictures, and decide for yourself which lens range best meets your needs.
paulj