1. A prime lens is one that has a fixed focal length; when you look through your viewfinder, what you see is what you get. If you need to recompose your shot, you have to move. No adjusting the lens to suit the scene, you have to change your position to change the scene.
2. A prime lens has fewer moving parts, so its lighter than most lenses, nice on a long walk.
3. A prime lens can have a larger aperture, which means more photos in low light without a flash, and better background blur, or "bokeh", excellent for portrait work.
4. Fewer glass elements inside the lens = less light distortion = sharper images, richer color detail.
Pros: Low light use, razor-sharp images, huge base aperture which allows for buttery-smooth background bokeh, light weight for all-day use.
Cons: Fixed focal length means, if you need to recompose your shot, you have to move. Sometimes, there's nowhere to move to and you can't compose the shot.
Overall: Specific uses (portraits, fast-action, low light). Incredible results, but not for every situation, and definitely not an "all-rounder" walkabout lens. And this lens is not crazy expensive. The Canon 50 mm prime starts at about $120 USD on B&H Video's website. That one's a bit on the cheap, plasticky-feel side, but the lens glass is just fine and takes great pictures. You can therefore experiment with a great focal length (50 mm) at a low price with that one. These shots were all taken with a Canon 85 mm prime, about $400.00
Oh, and one other thing. To get the nice outdoor shots, I find it has to be dusk or dawn. I'm not saying that these are good or bad pictures, but for what it's worth, they were taken at 07:00 in the morning, about an hour after sunrise.