Fluorescent willemite and calcite from Franklin, New Jersey, USA
Fluorescence is the emission of light by a substance that has absorbed light or other electromagnetic radiation.
It is a form of luminescence. In most cases, the emitted light has a longer wavelength, and therefore lower energy, than the absorbed radiation.
The most striking example of fluorescence occurs when the absorbed radiation is in the ultraviolet region of the spectrum, and thus invisible to the human eye, while the emitted light is in the visible region, which gives the fluorescent substance a distinct color that can only be seen when exposed to UV light.  
The pictures of our fluorescent minerals are made under a day-light filtered short-wave UV-C light source (we use two Philips special - TUV 25 watt G25T8 long life mercury lamps) and/or a long-wave UV-A light source (Philips TLD 18 watt).