It can do several things.
First, it is in the spectrum that a lot of proteins get energy from. Most of them, actually. UV above 350nm (UVA is good for corals).
Second, the input of true UV below the visible range of 400nm can be absorbed by the coral, have energy used and then spit back out at slightly lower energy, which can be in the visible range. If you want to see deep violets, purples and blues, then you will get better results using true UV light. All light that is used for energy will be emitted at lower energy, so you have to "aim low" with your targe.
Third, the gold-standard light source for reefing has a good amount of UV. Check out some charts from the best-of-breed MH bulbs like 20K Radium or 14k Phoenix from 350nm to 850nm and you will see both UV and IR that are not being considered essential after being forsaken for a decade of LED development.
Fourth, the "hubris of man." People discount UV because it cannot be seen. Most meters (including PAR meters) do not capture any of it and just focus on general lighting, which is were too many assumptions and information is gleaned from. Just because it does not have any real impact on humans generally leads to the backwards paradigm of having to prove that corals need it, rather than the correct way of thinking that adaptation and evolution have developed corals that use what is in nature.
In short, UV is important... it is one of the reasons that MH still illuminate and grow coral better than LEDs. More and more LEDs are getting true-UV every - people are enjoying these lights better than previous generations.