Most photoluminescent events, in which a chemical substrate absorbs and then re-emits a Photon of light, are fast, on the order of 10 nanoseconds. However, for light to be absorbed and emitted at these fast time scales, the energy of the photons involved (i.e. the wavelength of the light) must be carefully tuned according to the rules of quantum mechanics to match the available energy states and allowed transitions of the substrate. In the special case of phosphorescence, the absorbed photon energy undergoes an unusual Intersystem crossing into an energy state of higher spin multiplicity (see Term symbol), usually a triplet state. As a result, the energy can become trapped in the triplet state with only quantum mechanically "forbidden" transitions available to return to the lower energy state. These transistions, although "forbidden", will still occur but are kinetically unfavored and thus progress at significantly slower time scales. Most phosphorescent compounds are still relatively fast emitters, with triplet lifetimes on the order of milliseconds. However, some compounds have triplet lifetimes up to minutes or even hours, allowing these substances to effectively store light energy in the form of very slowly degrading excited electron states. If the phosphorescent Quantum yield is high, these substances will release significant amounts of light over long time scales, creating so-called "glow in the dark" materials.
One measure of quantum numbers is the spin multiplicity (for a quick definition see Term symbol). A singlet excited state results when an electron is promoted while conserving its spin (an "allowed" transition). Relaxation back to the ground state is very fast because the multiplicity doesn't change. Transition to the triplet state involves a "forbidden" spin flip (electrons cannot exist in between the two states in a molecule) to produce the triplet. This phenomenon is known as inter system crossing (ISC) and is kinetically slow, but thermodynamically favorable (the triplet is lower in energy). Once in the triplet state, relaxation back to the ground state necessarily involves another spin flip to avoid violating the Pauli exclusion principle, which is again kinetically slow, but thermodynamically favorable. In some cases this energy is dissipated by the emission of a photon corresponding to the energy difference between the triplet state and ground state, but often it is dissipated vibrationally (see Phonon). The ratio between these two phenomena for a single molecule is known as the quantum yield of phosphorescence. Since the triplet state is lower in energy than the singlet excited state, the light is lower in energy (red-shifted) than if it had been emitted from a singlet excited state. Many compounds emit both from the singlet and triplet states and by measuring the difference in wavelength between the two the energy difference between the excited states can be calculated.
There are many facets to emission from triplet excited states and many people have spent entire careers studying the phenomenon. As one example, a process known as delayed fluorescence occurs when two triplets encounter each other (by delocalization in the solid state or encounter of two species in solution or the gas phase) and additively annihilate to produce one singlet excited state of higher energy. If this state then emits light it will be of the shorter wavelength associated with Fluorescence emission, but on a time scale appropriate for phosphorescence.
Kurt Nassau. The physics and chemistry of color, the fifteen causes of color. Wiley, 2001.