Fluorescence is a phenomenon present in around 1/3 of all diamonds. This causes them to glow under ultraviolet (UV) light, which is abundant in natural daylight and also in some artificial lighting. Diamond fluorescence is usually blue, but can shift in almost any color and is due to small amounts of the element boron which are present in the stone.

Whereas fluorescence is a debated subject for white diamonds, since it can render diamonds with a lesser color whiter, and contrarily render white diamonds of a good color ‘milky’, the situation is a different one for natural color diamonds. Fluorescence can enhance or change the color of a natural color diamond in magnificent ways, and is then considered as purely positive. A green diamond with a strong green fluorescence for example, is beautiful as the fluorescence enhances the color. A pink diamond with a blue fluorescence will appear gorgeously purplish.
The most famous and clear example is maybe the yellow and orange diamonds from Brazil, which often have a very strong green fluorescence. This creates wonderful color effects, and gives the impression that the diamonds are glowing.
It is of course a matter of taste, whether you like fluorescence in some colors or not, but in any case it is important to keep in mind that for natural color diamonds, the presence of fluorescence is not considered as a negative thing.