By definition, your eyes can't see UV, but ordinary film can, and many CCDs can as well, although to a much lesser extent than film. In theory, there's something to be gained by filtering UV out of the picture. Due to the very short wavelengths involved (below 400 nm), the UV band carries more than its fair share of atmospheric scatter. Scattered UV light can cloud distant backgrounds and impart an unwelcome bluish cast in film images. UV contamination tends to be most problematic at very high altitudes (well over 10,000 feet) and over long stretches of water.
So much for theory. In practice, these theoretical UV filter benefits simply don't show up on the digital side. Under nearly all conditions and for nearly all cameras, UV filters are a waste of money and a potential source of flare for digital photographers.