Fluorescence is some very cool quantum stuff happening right in front of you. Electrons in the molecules of some phosphor are getting all excited by some radiation (in this case UV), and letting off that energy in the form of visible photons.
The specific phosphor determines the energy of the photons released. Which is to say, the color. Phosphors are big business and can be found in everything from copier paper to television screens. Well, old-style television screens anyway. Get off my lawn, you LCD whippersnappers!