I'll not go into the optics of these and telling you how they work is a bit pointless - except that they work best at 90 degrees to the sun and reduce the light coming into your camera by about 2 stops.
What you need is to actually see the difference between a picture taken with the filter and one without. Both of the following pictures have been taken as JPEGs in camera with no post processing.
This is the original without the filter. It's OK but the sky is boring and the sea has a lot of glare.
This is with the polariser on. You can immediately see that the sky has changed to a more contrasty blue and the clouds are more interesting. The sea has lost it's glare and again becomes a deeper blue. The overall image is more pleasing and it's one of the very few effects that Photoshop has trouble replicating. If you are ever going to buy a filter this is the one.
One thing I would say is not to buy a cheap one as they don't work that well and it's a total waste.