Basically a UV filter is just that. It blocks ultraviolet rays to some extent. People primarily use them however for protection for their lenses, that way if you accidentally bump it against something, hopefully you will scratch or break the filter and not an expensive lens. I've never really used them much until I got a couple of expensive lenses. I recently bought one for a sigma lens I have b/c I figure a $50 investment is worth protecting a $700 lens. I also have one for my 50mm prime lens for the same reason though it was considerably less expensive.
Polarizing filters allow you to saturate some colors (like the deep blue of the sky or the ocean) and reduce some reflections on surfaces like water and glass. I think they all have a rotating ring (at least my B+H one does) and the amount of the effect can be increased or decreased as you rotate the filter depending on your orientation to the sun. You are supposed to use a circular polarizer if you have an autofocus lens, but the science behind this escapes me at the moment.