Persistent luminescence (a.k.a phosphorescence, afterglow, or Long Lasting Phosphorescence (LLP)) is the name given to the phenomenon found in materials which glow in the dark after the end of an excitation with UV or visible light - mainly phosphors such as silver-activated zinc sulphide or doped strontium aluminate. They typically glow a pale green to greenish-blue colour. They are routinely used in toys, watch dials, luminous paints, safety signs etc.
The phenomenon of persistent luminescence has been known to mankind for over a thousand years. Descriptions have been found of ancient Chinese paintings that remained visible during the night, by mixing the colors with a special kind of pearl shell. The first scientifically described observation of persistent luminescence dates back to 1602, when shoemaker and alchemist Vincenzo Casciarolo discovered the famous Bologna stone. The curious glow of this stone was described by Fortunius Licetus in the Litheosphorus Sive De Lapide Bononiensi in 1640, and was most probably caused by barium sulfide present in the rock. Natural impurities in the stone were responsible for the long duration of the afterglow."
Source : Materials, Volume 3 Issue 4
It has been known since the 1950s that the phenomenon involves so-called 'energy traps' (such as electron or 'hole' traps) in a material, but the an exact explanation of the underlying physics is still lacking.
The overall mechanism of the persistent luminescence is now quite well agreed on to involve the formation of traps followed by a subsequent thermal bleaching of the traps and emission from the Eu2+ sites. Despite the seemingly simple stoichiometry and structure of the alkaline earth aluminates, the determination of persistent luminescence mechanisms seems to present a very complicated problem. Accordingly, no general agreement has been achieved on the detailed mechanisms involved and several interesting and even exciting mechanisms have been proposed. Especially, the mechanisms resulting in the prolonged and enhanced afterglow when R3+ ions have been introduced into MAl2O4:Eu2+ as co-dopants are either ignored or are contradictory.
Source : Persistent luminescence phenomena in materials doped with rare earth ions Journal of Solid State Chemistry 171, 114–122/
Further reading : Wikipedia