Bladerunner is the designated name given to those police detectives who are specially skilled in the use of the Voight-Kampff machine and whose specific function is to track down and eliminate any replicants that manage to escape into human society and attempt to pass as real human beings. The official name of the Blade Runner Division is Rep-Detect.
The beginning of the Bladerunner movie gives further information on the history of Bladerunners: "After a bloody mutiny by a NEXUS-6 combat team in an Off-world colony, Replicants were declared illegal on earth — under penalty of death. Special police squads — BLADERUNNER UNITS — had orders to shoot to kill, upon detection, any trespassing Replicant."
Blade runners usually do not wear uniforms and are licensed to carry concealed weapons. The legal authorities of blade runner units obviously reach far beyond those of regular police units. Deckard, Holden, Gaff and Bryant are Bladerunners.