1/ Saturating colors and adding contrast
Polarizing filters reduce most of the reflected light in the photographed scene when rotated to a particular angle. It helps saturating the colors and increasing the contrast. It also reduces the haze in the atmosphere. That’s why images taken with a polarizing filter have richer colors and more contrast.
2/ Darkening the sky and emphasizing clouds
The maximum degree of polarization is 90° from the sun, so it’s quite easy to figure out that when you shoot with the sun on your right or left side, the polarization effect will be the strongest. This can cause problems especially when shooting wide-angle lenses during sunrise or sunset, while the sun is low above the horizon, because the more polarized areas of the sky will be much darker.
You can fix this problem by rotating the filter until you reduce the polarizing effect. With a telephoto lens it’s not an issue, as you are photographing only small sections of the sky.
3/ Reducing reflections
One of the biggest advantages of polarizing filters is without a doubt the reduction of reflections, especially when shooting in a wet, rainy environment. When you rotate the filter to maximum polarizing effect, you get rid of the reflection on water surface, foliage and rocks,so you saturate the colors nicely and add more contrast to the scene. It is impossible to substitute this effect in post-processing.
4/ Lengthening the exposure time
Polarizing filters reduce the amount of light coming to your lens, which is a disadvantage. However, on the other hand, it can be quite useful when shooting rivers or waterfalls, because it helps to blur the water without the need of an ND filter.
Of course, you can live without a polarizer, but if you want to achieve the special “pop” in your images, I’d highly recommend to get one. Especially, if you are into shooting creeks, rivers and waterscapes in general.