Hydroxyapatite is the main component of tooth enamel. It contains phosphorus in the form of phosphates, pyrophosphates etc. that are found to exhibit the the property of phosphorescence. But why don't the teeth glow in the dark ?
Just to add a little more on the interface between optics and dentistry:
Whilst teeth do not phosphoresce, they do in fact autofluoresce.
The differential auto fluorescence of healthy tooth and carious tooth has been used for the early diagnosis of caries. (Gugnani N, Pandit IK, Srivastava N, Gupta M, Gugnani S. Light induced fluorescence evaluation: A novel concept for caries diagnosis and excavation. J Conserv Dent 2011;14:418-22 and http://www.opticsinfobase.org/boe/abstract.cfm?uri=boe-2-1-149)
To see teeth glow, or rather, fluoresce, they should be illuminated with short wavelength light, like blue light (wavelength 450 nm) and the teeth will glow green, which will be visible if the the blue light is filtered out.
Firstly, phosphorus does not exhibit phosphorescence on its own (don't let words mislead you, they often don't mean what they seem like): See http://en.wikipedia.org/wiki/Phosphorescence#Materials and http://en.wikipedia.org/wiki/Phosphor#Standard_phosphor_types
Even if phosphorus did do so on its own, it would not do so in the body because it is always (almost always?) present as phosphate (PO4-), and this again is most often incorporated in other compounds such as nucleotides.
Teeth are made up of 3 substances. Enamel, dentin and cementum. Inside is the pulp. The best chosen answer is incomplete. Enamel fluoresces and undergoes phosphorecense but dentin of teeth is three times more phosphorescent than enamel. Phosphorescence is a specific type of photoluminescence related to fluorescence. Unlike fluorescence, a phosphorescent material does not immediately re-emit the light radiation it absorbs. The slower time scales of the re-emission are associated with "forbidden" energy state transitions in quantum mechanics. As these transitions occur very slowly in certain materials, absorbed radiation may be re-emitted at a lower intensity for up to several hours after the original excitation. When exposed to light sources containing UV components are turned on teeth, the fluorescence of human teeth gives them the quality of vitality, and they exhibit a fluorescent emission with a peak of 440 nm observed peak light. (bright blue hue) Because of dentin's atomic composition contains special collagen and mineral matrix phosphorescence allows it to collect light photons slowly to change tooth color. In this way, natural tooth color can be used as a measure of oral health and health of the brainstem which innervates the dentition. Dental OCT is now used in this way. Optical coherence tomography (OCT) is based on low-coherence interferometry, typically employing near-infrared light as its source because it deeply penetrates tissues with water. Water is the ideal chromophore for red light. The use of relatively long red wavelength light allows it to penetrate into the scattering medium of teeth and the pulp. Using light this way, OCT can provide “optical biopsy” without the need for excision and processing of specimens as in conventional biopsy and histopathology. Application of OCT in dentistry has become very popular since 1990. This is why in my Redox Rx blog I have used pulp testing as a modern redox variable for human health. It is from the dentinal pulp where light is released from cells and collected into the atomic lattice of dentin to change its frequency and this changes its color we observe. Tooth color can be used a health metric. So for these reasons the accepted answer is quite incomplete. We have known about tooth phosphorescence since 1941 as published in pubmed.