BUR is the acronym for Built-Up Roofing, so called because it is field assembled using alternate layers of roofing "felt" and asphalt. It is one of the oldest systems in the modern roofing industry and provides a certain level of insurance against mechanical damage by virtue of the multiple layers. The felts themselves are not watertight and the resistance to water entry is provided by the layers of asphalt.
Previously considered the least expensive roofing system, the current rapid increase in the price of asphalt is diminishing the differential in cost between BUR and some of the Single Ply Systems. Also the requirement in California that some roofs have a reflective and heat emissive membrane has resulted in the BUR manufacturers' producing white surfaced materials to meet this requirement. These white BUR's are more expensive than some of the single ply membranes which have always been inherently reflective.
Benefits: Multiple layer redundancy favored by some. Disadvantages: Typically a higher maintenance requirement than competing systems. With high asphalt costs the perceived price advantage has severely eroded.