There are two cases where you really need the resolution independence: if you have a really high-resolution monitor (if you've tried some of the recent high-end laptop screens, the text and things are too small for comfort) and if you have a problem with your eyes (in which case even a fairly normal screen makes things look to small to see clearly). In either case, you want everything to look bigger, including buttons and scroll bars, so they're easy to use.
Basically, the whole point is to make everything on the screen bigger without losing quality. Apple have made almost all of the interface in leopard so that it can be bigger without getting blurry (which is why the icons are now massive), and text will always look good.
Things like photos and most web graphics will always blur though, because the picture is stored as different coloured dots, rather than a description of the shape. Make dots bigger, and you just get big dots, not more detail, and you either get big coloured squares, or you blur it. There are ways of making a photo bigger without it blurring, but they're generally slow, and never that good (because you can't fill in the gaps between the dots without knowing what's really there - you can only guess).
Resolution independence is there in leopard, but it's not really finished yet. You can turn it on (if you have the developer tools installed), and some things will work fine, others (like the finder) look pretty buggy. It's usable though.