In the last quarter of the 19th Century, the City of Brooklyn was comprised of much of today's "Downtown Brooklyn". Brooklyn suburbs were areas such as Midwood, Bensonhurst, and if you were wealthy and didn't mind a long ride, the ocean areas of Brighton Beach, Manhattan Beach and Coney Island. Owners of the major hotels at the time, like the Brighton Beach Hotel and the Sea Beach Palace Hotel, were looking for new ways to attract new customers. As a result, they helped finance new steam railroads to the beach, but because each acted on his own, the steam railroads that "grew up" were disjointed, concentrated in the western and southern portions of Brooklyn, and really weren't built for the rapid transit that we know of today.
Meanwhile, another company, the Brooklyn Union Elevated Railroad Company, was responsible for the creation of the first Elevated lines that fanned out of the City of Brooklyn. New areas of the land would become accessible, and with trains running over the Brooklyn Bridge to Park Row as early as September 1883, now the commerce center of New York would be a shorter ride away for these Brooklynites.
The force that created rapid transit in Brooklyn was the American model of free enterprise. The first company to create the route would reap all the profits from passengers using that route.
Eventually, all these companies and lines (including the Nassau Electric, the Coney Island & Brighton Beach, the Brooklyn Elevated, the Brooklyn Union Elevated, the Prospect Park & Coney Island, the Brooklyn, Bath & Coney Island, and the Coney Island El [Sea View RR]) became the Brooklyn Rapid Transit Company, which eventually began running these lines as a unit. With the BRT came electrification and rapid expansion. Eventually the BRT would become a competitor to the Manhattan-oriented Interborough Rapid Transit Company (IRT), and would be instrumental in future New York City subway expansion. Like the IRT in Manhattan, the BRT was the only player in Brooklyn.