I know what a polarizer does to the light, and how it works technically (filtering out some of the oscillation directions of the electromagnetic radiation), and also how this affects pictures (removing or enhancing reflected objects, and providing a clearer picture in general).
I was wondering how these facts are related, i.e. how come that polarizing light makes the image more defined and clearer, and colors more saturated. Can someone explain this to me?
Wikipedia and this other answer may help you.
I think your question could easily be answered by a quick google search, where you would find links as How, When, and Why to Use a Polarizing Filter or this one that addresses color saturation and sharpness. It depends on how much you want to know and which part of "how it works" you're curious about.
Glare is the enemy of contrast. When you get reflections off of things in the scene that are the color of the light source rather than the color of the object being blocked, this results in a loss of detail. Additionally, this can end up overloading the lens due to the inability of most lenses to deal well with extremely bright sources of light within the shot or can throw off exposure in general, thus reducing the overall contrast and quality of the shot.
By removing the glare from the shot, contrast is increased and image quality is improved. The most pronounced examples are things like looking at the surface of water. When you aren't using a polarizer, the water reflects the light and/or the sky and no detail can be seen. When you put on a polarizer, it suddenly looks like we think of water looking and you can clearly see the details under the surface with the glare removed.
Just a little more explanation: Light reflecting off a colored surface (say a Pizza Hut red roof) has two parts. Whatever reflects off the surface gets no color and is reflected like a mirror. Some of the light which strikes the surface actually penetrates a few molecules deep and comes back out the color of the Pizza Hut roof, red. When you photograph the roof the camera sees both the red light (from the paint molecules) and the surface light (approximately white) and records a pale red color. A side effect of the reflection is that what is reflected from the surface is polarized and what comes from the molecular penetration is not so....if we turn our lens-mounted polarizer to block the polarized light all that is left is the red light and POOF we have a bright colored Pizza Hut roof. New Pizza Hut roofs are black so I will need to revise my explanation soon.
