Switch off a UV lamp over a tray of fluorescent minerals and almost everything goes dark instantly. Occasionally something does not. A specimen keeps glowing for a second, or ten seconds, or in rare cases minutes. That is phosphorescence, and it is a genuinely different physical process.
What fluorescence does
Ultraviolet light delivers a photon to an electron in the crystal, kicking it to a higher energy state. The electron falls back almost immediately, releasing a photon of lower energy, which is visible light. The whole round trip takes nanoseconds. Cut the UV and the glow stops within a fraction of a microsecond. The full mechanism is in why some rocks glow under UV.
What phosphorescence does differently
Sometimes the excited electron does not drop straight back. Instead it crosses into a state from which the return to the ground state is quantum-mechanically forbidden, or at least strongly discouraged. Forbidden here does not mean impossible, it means improbable, so the transition happens slowly.
The electron sits in that state as though in a waiting room, and leaks back gradually. The result is light emitted over milliseconds to minutes rather than nanoseconds. The energy is genuinely stored, briefly, in the crystal.
Some materials go further, trapping electrons at lattice defects from which thermal energy at room temperature slowly frees them. That is persistent luminescence, the effect behind glow-in-the-dark paint, which can run for hours. Modern glow pigments are engineered strontium aluminate, not a natural mineral, but the principle came from studying minerals.
Minerals that do it
Willemite from Franklin, New Jersey is the classic. Certain calcites phosphoresce, as do some fluorites, some diamonds, and some scapolite. It is worth stressing that fluorescence and phosphorescence are both properties of a specific specimen, not of a species. Two calcites from two localities can behave completely differently, because the effect depends on trace activator ions, usually manganese, uranium or rare earths, at parts-per-million levels.
Franklin, New Jersey is the most famous fluorescent locality on Earth and sits in the same state as the trap rock quarries described in Paterson and the Watchungs, though the geology is entirely different: metamorphosed zinc ore rather than volcanic rock.
Two related effects worth knowing
Thermoluminescence. Some minerals that have accumulated trapped electrons from natural radiation over geological time will release them as light when heated. Fluorite gets its name from this family of behaviour, as covered in fluorite. Archaeologists use thermoluminescence to date fired pottery: firing resets the clock, and the accumulated signal since then gives an age.
Triboluminescence. Light produced by mechanical stress. Crush quartz or sphalerite crystals in a dark room and you can see flashes. Rubbing two quartz pebbles together hard enough produces a visible glow through the stone.
How to actually test for it
You need a properly dark room, a few minutes of dark adaptation for your eyes, and a UV lamp you can switch off cleanly. Shortwave UV excites more minerals than longwave but requires real eye and skin protection, since shortwave UV causes photokeratitis and burns. Proper UV-blocking goggles are not optional.
Illuminate for thirty seconds or so, then cut the lamp and watch. Most things will vanish. If something lingers, you have found a phosphorescent specimen, and it is worth recording which lamp and how long, because that is real data about the piece. We have not tested any of our current stock for either effect and so make no claims about it, for the same reason set out in the provenance post: untested is not the same as negative, but it is not a selling point either.

