This stretch of wall running down Third Avenue in Brooklyn, between First and Third Streets, is a remnant of Washington Park, a professional baseball park that once stood on this site. For a while, it was commonly believed that this wall dated back to the last couple of years of the 19th century, when the Dodgers* played in Washington Park: in 2007, the NY Times said that the wall "is believed to be the oldest standing piece of a major league ballpark in the country."
In recent years, however, another theory, one more convincing and well-documented, has made its way to the fore, arguing that the wall is a remnant of Washington Park, but that it was constructed in 1914, as part of a more modern facility built for the Tip-Tops of the short-lived Federal League, after the Dodgers had decamped to Ebbets Field.
Either way, it's a physical link to big-league baseball in Brooklyn, and there was a bit of controversy when Con Ed, who has owned the property since the 1920s, decided to demolish part of the wall in 2010. They left what was generally considered to be the "historic" portion in place, however, including the windowed section to the right, which some still believe dates back to the days of the Dodgers.
* The Dodgers had no official team nickname for the first few decades of their existence; their legal name was the Brooklyn Base Ball Club. During their time here in Washington Park, they were known informally as the Bridegrooms, the Superbas, and the Trolley Dodgers.