Phosphorescence is a type of photoluminescence related to fluorescence. When exposed to light (radiation) of a shorter wavelength, a phosphorescent substance will glow, absorbing the light and reemitting it at a longer wavelength. Unlike fluorescence, a phosphorescent material does not immediately reemit the radiation it absorbs. Instead, a phosphorescent material absorbs some of the radiation energy and reemits it for a much longer time after the radiation source is removed.
In a general sense, there is no distinct boundary between the emission times of fluorescence and phosphorescence (i.e.: if a substance glows under a black light it is generally considered fluorescent, and if it glows in the dark it is often simply called phosphorescent). In a modern, scientific sense, the phenomena can usually be classified by the three different mechanisms that produce the light, and the typical timescales during which those mechanisms emit light. Whereas fluorescent materials stop emitting light within nanoseconds (billionths of a second) after the excitation radiation is removed, phosphorescent materials may continue to emit an afterglow ranging from a few microseconds to many hours after the excitation is removed.
There are two separate mechanisms that may produce phosphorescence, called triplet phosphorescence (or simply phosphorescence) and persistent phosphorescence (or persistent luminescence). Triplet phosphorescence occurs when an atom absorbs a   high-energy photon, and the energy becomes locked in the spin multiplicity of the electrons, generally changing from a fluorescent "singlet state" to a slower emitting "triplet state". The slower timescales of the reemission are associated with "forbidden" energy state transitions in quantum mechanics. As these transitions occur relatively slowly in certain materials, absorbed radiation is reemitted at a lower intensity, ranging from a few microseconds to as much as one second after the excitation is removed.
On the other hand, persistent phosphorescence occurs when a high-energy photon is absorbed by an atom and its electron becomes trapped in a defect in the lattice of the crystalline or amorphous material. A defect such as a missing atom (vacancy defect) can trap an electron like a pitfall, storing that electron's energy until released by a random spike of thermal (vibrational) energy. Such a substance will then emit light of gradually decreasing intensity, ranging from a few seconds to up to several hours after the original excitation.
Everyday examples of phosphorescent materials are the glow-in-the-dark toys, stickers, paint, and clock dials that glow after being charged with a bright light such as in any normal reading or room light.  Typically, the glow slowly fades out, sometimes within a few minutes or up to a few hours in a dark room.
The study of phosphorescent materials led to the discovery of radioactive decay.