It's a dance where the lighting is ultraviolet (UV) light bulbs. Most darkly colored objects will be invisible, but things like white shirts and people's teeth will appear to glow. You can also get specially treated fabrics that will show up well in UV light.
A black light dance is a dancing event held in a room that is quite dark but has lighting systems that reflect the color of the clothes you wear and other items in the room. In this dance, people are mostly advised to wear white, black or neon-colored attires. The music played in such dance parties is mostly rave and dance. Learn more about it from http://www.ehow.com/facts_5633256_black-light-dance_.html.