Fluorescence is the visible light some diamonds emit when they are exposed to ultraviolet (UV) light.  Fluorescence is a common occurrence in diamonds, but it is only when the fluorescence is medium to strong that it may affect the appearance of the diamond.  The stone will have a hazy appearance sometimes referred to as "milky".  Generally the colour emitted by the fluorescence is blue, but on rare occasions it can be other colours such as yellow or white.