What is the importance of UV radiation to pet reptiles?

The Need for UVA Lighting For Reptiles

Reptiles can see much farther into the UVA spectrum than humans… more so than can be provided by "regular" light bulbs. This allows them to perceive patterns and colors beyond what we can see. Depriving them of a large portion of their visible world can cause serious health issues, as well as physiological and behavioral abnormalities.

Leaving a reptile blind to half of their environment causes unnecessary stress, which will generally affect their overall well-being. Lack of UVA light can impair a reptile's ability to recognize friend from foe. The UVA spectrum is used to recognize patterns of their fellow species from other animals, and plays a big role in helping them detect movement. It also helps them recognize their diet foods and generally stimulates the appetite by telling them what's good to eat. UVA also provides the visual cues that controls the basking instincts that they need to regulate their body temperature. UVA generally promotes more activity, foraging, social behaviors and reproductive activities.

The Need for UVB Lighting For Reptiles

UVB light controls the synthesis of vitamin D₃ through the skin, which is needed to metabolize and absorb calcium and other minerals. The need for UVB varies by species. Generally speaking, diurnal reptiles (active during the day) need UVB to manufacture vitamin D₃. Nocturnal species (primarily active at night) will typically meet their vitamin D₃ needs through their food source. Do your research on your chosen reptile.

Without enough vitamin D₃, reptiles can suffer from chronic calcium deficiencies leading to bone deformities. Vitamin D₃ is also important to proper organ development and regulating the immune system. Reptiles that do not get enough vitamin D₃ at a young age can even lose the ability to synthesize D₃ through UVB absorption at a later age. Most reptiles do not exhibit signs of these illnesses until they are quite advanced and beyond help, so do your research.

"Full Spectrum" Lighting

Another note of caution:

I have been to a lot of pet stores that sell reptiles as a side line, and received a lot of bad advice throughout. They simply do not know what they are selling, so you have to do your research. Manufacturers learned long ago that herp enthusiasts were being told to "use full spectrum lighting" so anything that might typically be considered broad spectrum is being marketed as full spectrum. The amount of UVA and UVB output by a fixture can vary greatly. The needs of different reptiles vary greatly. Supplements range from somewhat helpful to actively harmful in overdose situations. But this all goes well beyond the scope of this question.