This is not to be confused with Bioluminescence, a chemical reaction independent of any outside light source which happens inside the organs of a creature. Most popular among divers are the Copepods that erupt like stars at any disturbance, also interesting are the bioluminescent signals and lures of deep ocean creatures.
Luminescence is also a chemical effect, however it relies on an external light source that is stored and released slowly over time. A classic example is the glowing dial on your pressure gauge.
Fluorescence itself is not limited to animal pigments. Items like fluorescent lights in your home emit light when the phosphor coating inside is stimulated, although in this case not by a light source.
Many things fluoresce from peanut butter to flowers -- to scorpions. Even humans have fluoro-reactive proteins and the lighting equipment we use is very much like what you see used in Crime Scene Investigation adapted for underwater use.