Polarizing filters are used to manage light at wavelength scale, and if magnified could be likened to a series of microscopic slats. In use, as the filter is rotated, it either transmits or blocks the waves of light that are vibrating in particular orientations.
When light from the sun bounces of a flat non metallic surface, such as glass or water it becomes polarized - ie: all of the reflected light waves vibrate in the same plane. This reflected glare can be removed by the polarizing filter as it is rotated to the optimum position. In photographic terms this can render water or glass transparent, and gives the impression of saturating colors in a scene because much of the reflected glare from the subject is removed by the filter.
On a sunny day, much of the light in the sky is also polarized, and the filter will give a very strong blue effect when used at an angle close to 90 degrees to the sun any white clouds will stand out impressively against such a dark blue background.
Circular Polarizers spin the light waves so as not to confuse the internal optics of modern reflex cameras whereas linear polarizers work with the simpler optical systems in more traditional cameras.
This is the construction of a type of filter. The type of process used to create a filter can affect its price. Filters can be constructed out of regular glass that sandwiches a coloured gel in between or in high-end filters, raw elements are added to the molten optical glass so there is no risk of uneven colour or fading.
When placed in the optical path, many filters block a certain amount of light from reaching the lens. Filter factor relates to how much exposure compensation is required in order to adjust for this. Most cameras have TTL metering and will be able to do this automatically.