I love my polarizers, and use them often. But sometimes when I'm out in the field, people ask, "Why are you using a polarizer? I just do it in Photoshop." Here's an example of why you can't just do it in post.
I went to Hawaii in February to hang out with Norbert Wu and to shoot a big swell on the north shore. Here is a shot of Waimea Bay, taken without a polarizer. The sun is directly to me left, and is low in the horizon.
I put on a polarizer and took the same shot:
Although some aspects of the polarized image can be approximated in Photoshop, you cannot exactly duplicate the effect. Polarizers are used most commonly to reduce reflections, to saturate and darken the sky, to increase saturation in general, and to block out light in really strong sunlight. In the image above, the polarizer has darkened and saturated the blue sky dramatically while leaving the clouds bright white. The reflection on the water of the light-blue sky has been knocked out, too, darkening the water.
I don't really want to write an article about how polarizers work, but I can offer some tips for shooting with a polarizer. Luminous Landscape has a good article that talks practically about polarizers from a non-technical standpoint, and you can do a google search for more (although most of the articles that come back are sort of lame).
One thing to remember is that polarizers are most effective when the direction of sunlight is orthogonal to the direction your lens is pointing. During mid-day when the sun is directly overhead, polarizers are effective when you shoot in almost any direction (except upward). However, at sunrise or sunset, polarizers are only going to be effective if you are shooting perpendicular to the direction of sunlight. This is why your polarizer does nothing except block out light when you shoot a sunset with it. Take off your polarizer when shooting sunsets!
I also see people shooting inside with polarizers. Polarizers knock out a lot of light, and it's hard to shoot with them -- even outside -- if there isn't enough light. These same photographers will even put on a flash to compensate for the reduced light, just because they are too lazy to remove the filter (!). I don't understand this at all; it only takes a few seconds to remove a polarizing filter. Just take the damn filter off! :)
Speaking of exposure, circular polarizers are supposed to allow cameras that meter through the lens to expose accurately. However, I almost always find that I have to overexpose images even when I am using a circular polarizer. To compensate, I typically set my exposures around one stop over what the camera's metering system recommends.
You'll also notice that there is vignetting in the image above. This is a problem with wide-angle lenses and screw-on filters, in general. The image was taken with a Canon 24-105/4L IS lens, which I've found always vignettes at 24mm if I am using a filter. This could probably be solved by using ultra-thin filters... which I don't use because I like being able to put a lens cap on when the filter is attached.