Yes, Brooklyn is a huge place. It's NYC's largest borough with an estimated 2014 population of 2.62 million people living in a 71 square mile area. If it were its own city, only Los Angeles and Chicago would be larger by population, although both would pale in comparison with Brooklyn's density.
When I was up there, I stayed in Queens, which is the largest borough by land area and second largest by population. A lot to see but very hard to do in a week's time period. I'll definitely have to get back up there to do some urban exploring at some point in the future.