Technically speaking, Rob Van Beurden defines fluorescence in diamonds as:
In much simpler terms, fluorescence is the tendency for a diamond to absorb radiation from an ultra violet light and emit it as visible light. The most common colour of fluorescence is blue.
Prevalance of Fluorescence
A diamond's fluorescence can be given a grade from "none" to "very strong", with faint, medium and strong in between.
Fluorescence can either be graded manually, or with the aid of machines such as Sarin's Colibri.
Colour vs Fluorescence
Blue fluorescence has the ability to "cancel out" or reduce the tint of more yellow (lower colour grade) diamonds. A GIA survey even found that more fluorescent, especially more yellow and therefore lower graded diamonds were favoured over their non-fluorescent counterparts.
Effect on Pricing
It is generally accepted that the greater a diamond's fluorescence, the less it will sell for. One, seemingly flipant explanation given is that the lights used in the GIA's grading laboratory emit a small amount of UV light, thus giving diamonds with blue fluorescence a higher colour grade. However, it must be remembered that UV light is present in almost all environments.
This table shows that for diamonds with higher colour grades, fluorescence is detrimental to a diamond's price, whilst for lower graded, more yellow diamonds, fluorescence can increase the price of a diamond.
Cloudiness or Oiliness Caused By Fluorescence
A very small number of stones with strong or very strong fluorescence appear "oily" or "cloudy". Whilst this is quite rare, it is always advisable to look at a stone with strong or very strong fluorescence before purchasing.
Other Colours of Fluorescence and Phosphorescence
Whilst very rare, diamonds can emit yellow or orange fluorescence, whilst some diamonds may even continue to glow after the UV light source has been removed. These diamonds display phosphorescence.