What is a diamond's fluorescence?

Fluorescence refers to the effect that is seen in some gem-quality diamonds when they are exposed to long-wave ultraviolet light (such as the lighting frequently seen in dance clubs). Under most lighting conditions, this fluorescence is not detectable to the eye. However, if a diamond is naturally fluorescent, it will emit a soft coloured glow when held under an ultraviolet lamp or "black light." Fluorescence is not dangerous to the diamond or to the wearer; it is a unique and fascinating quality that occurs naturally in a number of gems and minerals.

Fluorescence has no noticeable effect on your diamonds appearance. Fluorescence is the light that some diamonds emit when they are exposed to ultraviolet rays. The term fluorescence on a certificate refers to the strength, or intensity, of the diamond’s reaction to UV rays. Fluorescence is actually a common characteristic for diamonds. However, only a very small percentage of these diamonds has strength of fluorescence that may have a visible impact on the appearance. This can only happen (but even then not always) when a diamond has a strong or very strong fluorescence. A low or medium degree of fluorescence has no impact on the diamond’s appearance. In reality there are many customers who prefer that the diamonds have a light or medium fluorescence. Some even ask for strong fluorescence. The preference to buy a diamond that exhibits fluorescence is a personal one, as a diamond’s appearance must be taken as a whole. Other factors can influence colour appearance more strongly than fluorescence, such as how the diamond has been cut, whether the diamond is viewed in natural or artificial light, and even what you’re wearing on any given day.

Please read the following article by GIA for further reference.