When a material absorbs light, usually ultraviolet or blue, and gives it back out at a longer, visible wavelength.
The emitted light adds to ordinary reflection, so a fluorescent surface can return more visible light at some wavelengths than falls on it, which is why fluorescent colours look brighter than any ordinary paint.
Fluorescence stops the moment the exciting light is removed; phosphorescence, which continues to glow, is a different effect.
Optical brighteners in paper and detergents fluoresce blue under daylight's ultraviolet, making white look whiter.
Fluorescent materials measure and look very different depending on how much UV the light contains, which complicates matching and printing.