A black light is an ultra violet light that creates the appearance of glowing objects when activated. The ultraviolet light is detectable when hit by a specific amount of radition. Black lights are undetectable by simply our eyes alone. Specific materials called Phosphors change the energy to make the ultra violet radioton detectable by the human eye. This would be the reason why our white shirts glow under a black light, but not under regular lighting, or in the daylight. Teeth and fingernails naturally have Phosphors, making them detectable under the black light. Basically, the higher Phosphor content, the more detectable under a black light.
This is a video of Ross, from "Friends", and his teeth under a black light :)