This item of kit is mainly for the SLR user but some types of polarizing filter can but fitted to compact cameras.
A polarizing filter can be used both in colour and black and white photography. They work by controlling the amount of light reaching the lens, or a least the direction that the light is traveling in, as by cutting out some reflected light the filter does some amazing things like; darkening the sky, removing reflections from water, and making foliage more colourful, colour saturation overall is also significantly enhanced.
The benefits of polarizing filters are largely unaffected by the move to digital photography, software post-processing can simulate many other types of filter, but most of the optical effects achieved by using a polarizing filter simply cannot be replicated in software.
In my opinion this is one of the most useful items of kit you can have, i always have one on my wide lens and have found that taking more than one shot with it adjusted differently gives me more options when I'm at home working on the shots.
The next 2 photo sets show the same scene both with and without a polarizer, no other settings were changed.
In this shot the sky has been darkened, making the clouds stand out more and the grass is more vibrant.
In this shot there is less reflection and glare on the water and wet rocks, giving the colour in the image time to shine through.