The great American astronomer Edward Emerson Barnard spent a large chunk of his career putting together a extended list of dark nebulae -- a list of everything that was an inky blot against the night sky. This list is still used to refer to dark nebulae in the same way that the Messier List is used to refer to nebulae and other bright things that weren't clearly stars.
A Barnard object is refered to as 'Barnard x' or 'Bx', where 'x' is the number of the object as it appears in Barnard's list. Barnard published his original list in 1919, in the Astrophysical Journal. His paper was entitled On the Dark Markings of the Sky with a Catalogue of 182 such Objects. He continued to expand his list throughout his career.
By the time of his death in 1923, he had collected 366 Barnard objects; the list is now closed. In 1962 Beverly Lynds published the Catalogue of Dark Nebulae, so you will sometimes hear people refer to "Lynd-Barnard" objects. These lists have since been subsumed into the New General Catalogue (commonly called the NGC / IC catelogue), but astronomers will still often refer to these bodies as Barnard's objects.