An Insurance Policy for Your Lens
The clear UV filter screws onto the front of your lens.
Imagine that you're on a hike and grind the front of your lens against a sharp rock. Without a UV filter in place, you're going to have to replace the lens.
This can cost anywhere from £300 to £3000 (depending upon the lens).
With a UV filter in place, the only thing you've damaged - and need to replace - is the filter. Approximate cost: £10-£15.
What's the Catch?
Since the logic behind a UV filter makes so much sense, why doesn't everyone use them all the time?
Most people do, but there are some professional photographers who argue that a UV filter affects the quality of your photos regardless of the filter's clarity.
This argument also makes sense: for the clearest possible images, don't put something on the front of your lens and leave it there all the time.
In the end, the answer has a lot to do with how you use your camera:
If you enjoy taking your DSLR on your travels, hikes and other excursions, where there is a high chance of smacking the front of the lens on something, then always use a UV filter
If you take photos in more controlled environments (indoors, studio, etc.) then you may opt to leave off the UV filter to ensure the highest possible image quality