UV light has a short enough wavelength that its energy matches the bond energy of organic molecules, so when they absorb a UV photon, they break. The bond strength is variable, depending on the other atoms nearby in the molecule and how much they take or give electron density to the bond in question, so the wavelength required to break a bond varies. However, it's usually well into the UV.
An interesting exception (there are many, but this one is just particularly relevant) is retinol. It's the stuff that makes carrots orange, but also, as you might think from the name, what's in your retina. It has a double bond, where two adjacent atoms share two electrons, which prevents them from rotating with respect to each other, so it's shaped like a paperclip. When a photon hits it, the double bond absorbs it, and one of the two bonds briefly dissociates and then reassociates, allowing the molecule to straighten out. This is how we see: that conversion from folded to straight on absorption of a photon is the mechanism for vision. (The enzyme with which it is associated comes in several different flavors, that slightly distort the molecule, and that changes the energy required to make this rearrangement happen. One bunch of enzymes make it red-green sensitive, another blue-yellow sensitive, one simply provides a highly sensitive measure of whether there are photons at all and results in low-light black-and-white vision. This is happening billions of times per second, and the process of replacing all those popped molecules is the most energetically demanding thing in our bodies, so our retinas suck up a lot of oxygen from blood.)