Herald Square was a plaza in New York City. The square was located north of Times Square on Upper Broadway. During New Year's Day celebrations, hundreds of celebrants would gather here to welcome in the New Year.
In The Big Good-Bye, on one New Year's Eve, Barney Kollecher, a police officer, had his fellow officers posted at this location. They were to keep the peace, and arrest petty criminals and bullies. (TNG: "The Big Goodbye")