Using a polarizer filter

A house in Russel, New Zealand.  The left was taken without a polarizer; the right used one.

Two shots, same building, same exposure.  The difference is the polarizer filter.  If you have never used a polarizer filter, you will be surprised by their usefulness.  It is an essential part of any well equipped photographer's arsenal.  And the good news is, they are not very expensive.
To really appreciate the difference in the two shots, I will take time to point them out.  The first is obvious; the sky.  Notice how the clouds stand out better in the second image.  Also the blues are darker and much more saturated.  This is not because it is blue, it is because of what the polarizer is doing.  We will get to that.
Take a look at the red roof.  The house had a vibrant red roof which starkly contrasted with its walls and windows.  The image without the polarizer does not capture that, but the one with the polarizer does.  Again, it is not a function of colour or hue; it is a function of what a polarizer does.
Another difference, more subtle, is the polarizer's effect on white balance.  Notice the right image appears a cleaner white.  The image on the left is flatter in contrast and has a certain hue of colour associated with it.  Polarizers remove some of the colour cast associated with blue skies.
OK - so it works.  The question is, "Why?"  The answer has to do with light coming in from the open blue sky.  Light from the sun vibrates in all planes, and they are not polarized.  That means that each ray of light vibrates at a random angle.  Polarizers do not let light pass though it that vibrate at a particular plane.  It will remove some light, which is why polarizer filters appear grey.  You have to give up about a stop of light.  But their benefits greatly outweigh this disadvantage.
Light reflected from open sky has a decidedly blue colour associated with it.  When it comes to earth it throws a colour cast on everything.  Whites and greys appear bluish, greens are much darker and the skies are brighter.  Put on a polarizer and look what happens.  That blue light gets pulled out so skies darken up, blue shades get removed, and colours appear the way they are meant to be.
Polarizers don't work all the time; they only work in situations where there is polarized light.  I take mine off indoors or during events which do not benefit from it.  There are times though, that it is great to have.