Polarised filters are an essential part of a landscape photographers kit. If I left home without mine I would have to return home to get it. A polarising filter works by reducing glare from reflective surfaces such as water, glass and shiny surfaces such as car bodies and wet rocks.
They also reduce light entering the lens and work as a neutral density filter which helps reduce shutter speed if you need a longer exposure such as on flowing water.
But there are some downsides to this piece of glass. If you are hand holding in low light then it's best to remove the filter because leaving it attached is only going to slow down your shutter speed and lead to a blurry shot.
Precaution is also needed with wide angled lenses as the filter will cause uneven lighting across the image making the sky unnatural.
Sometimes though we want to capture those reflections as in the images of the stepping stones above.
The non-polarised image has more contrast due to the glare of the reflected light making the stones more prominent in the scene, whereas the polarised image reveals what is under the water by filtering the reflected light.
The stones have no contrasting properties and are lost within the pool of water and the leading line of the path is not as effective.
Rainbows can also be problematic, who doesn't love a good rainbow picture.
Rainbows are effectively reflected light so it makes sense that we do not want to reduce that, we want to capture all that reflected colour in our camera.
So there are a few reasons for using one and not using one.
If you do actually purchase a polariser and I highly recommend you do, it's to buy a good quality one. There is no point having a good quality lens to then put poor quality glass in front of it.