Fluorescence becomes visible when you expose the diamond to UV light - it causes the diamond to glow, usually blue, but sometimes other colours too. Fluorescence is caused by gaps in the crystal structure of the diamond. The UV light excites electrons in the diamond and because of the gaps in the crystal structure these electrons can then vibrate causing the diamond to glow.
The diamonds are graded for the level of fluorescence from None, through to Faint, Medium, Strong and finally Very Strong. Higher levels of fluorescence can sometimes also cause the diamond to become milky or cloudy in sunlight. This reduces both the brightness of the diamond, and also the levels of fire in the diamond.
Unfortunately it is not as simple as saying that for example, any diamond with strong blue fluorescence will look milky or cloudy. It varies depending upon the diamond - if you were considering a diamond with higher levels of fluorescence it is definitely worth checking the diamond to ensure its appearance is not negatively affected by the fluorescence.
