Their duty is to identify, hunt and kill replicants who have arrived on Earth illegally, referred to as "retiring" them. The reason for the reference to them as "Blade Runners" was never explained in the film.
Known Blade Runners
Behind the Scenes
The term "Blade Runner" originates not from any works by Philip K. Dick but from a little known 1974 novella by Alan E. Nourse. This novel was called The Bladerunner and in the novel, the reason for the term is given. Bladerunners (the term is one word in this novel) are black market medical suppliers for underground physicians. The term appears to refer to the scalpel blade, a picture of a medical scalpel is prominently on the book cover illustration.