in photography, a polarizer is a filter with some specialized but important applications.
It is just a piece of polarizing materials, installed in a mount that allows it rotate - to get an idea of the effect, find some Polaroid sunglasses, hold them in front of your eyes and rotate them. If you are looking at a scene with polarized light components, you will notice that some things go dark and light - try with road surfaces, water, metal, and a clear sky.

A polarizer does exactly that, only it sits in front of your lens. What are its applications ?

  1. darkening skies. Landscape photographers have a real problem with the sky being too bright (read all about it in graduated neutral density filter), and part of the light that comes from blue sky is polarized. A properly oriented polarizer will darken the sky and leave the ground mostly alone.
    If overapplied, you get a surreal dark blue sky. Some people like it.
  2. killing reflections: shop windows, glass tables, glass walls all reflect polarized light. The polarizer can remove the reflected component.
    A typical application is taking a picture of something behind a shop window, or under water.
  3. document reproduction: again killing reflections, but in this case the concern is the specular highlights that light sources will produce on some types of paper stock, and on oil paintings.

polarizer issues: it eats one to two stops. If carefully used, it can lead to blotchy skies, particularly with wideangles.
Due to its rotating mount, it tends to be a thick filter. This can lead to vignetting with wideangles.