If a diamond has extremely strong fluorescence it can appear oily or cloudy, and this is not good.
Otherwise, it can improve appearance, especially in diamonds with faint yellow body color. See Fluorescence.
Besides, you can get a better deal for it. Some people like it because it adds some uniqueness to your diamond.
In 1997 the GIA conducted a study that challenged trade perceptions that UV fluorescence has a negative effect on diamond appearance. Their results support an older belief that strong and very strong blue fluorescence can improve appearance, especially in diamonds with faint yellow body color. Benefits of blue fluorescence in colorless to near-colorless diamonds was also evident in the study, bringing into question the trade’s lower ‘bid’ prices for moderate to highly fluorescent diamonds in the better colors.