Phosphorescence is the emission of a photon from the triplet state of a molecule. It lasts for a long time because the jump from triplet state to singlet ground state requires an electron to change spin, which is a quantum mechanically forbidden transition.

Many molecules can be excited by an incident photon to the lowest singlet excited state. If these molecules then emit light from this state, it is known as fluorescence. Sometimes, a process known as internal conversion may occur and the electron may drop down to an intermediate triplet state. Now, the electron is trapped because it needs to undergo a forbidden transition to reach the ground state. This is why phosphorescent material will glow for minutes after being exposed to bright light.

___________________ singlet excited state ____________
                                 \
 ^                                \ internal conversion
 |               |                 \
 |               |                  \
 |               |                 ___________ triplet state
 | excitation    | fluorescence            |
 |               |                         | phosphorescence
 |               |                         |
 |               v                         v
__________________________ ground state  _____________


An interesting experiment to try at home: Take an object that glows in the dark with the green phosphorescence. Charge it up with room light until it glows very brightly when you turn off the lights. Now, if you take a laser pointer (the red diode laser ones) and shine it on the object, you'll see a dark spot where the laser hit it. Instead of charging the phosphorescence up, its taking it away! This is because the red laser light is actually making the electron jump from the low energy triplet state back to its singlet excited state, where it then quickly decays back to the ground state. Red light has less energy than blue and green light so it is not strong enough to excite from the ground state to the excited state.