An NYPD helicopter is a helicopter owned and used by the New York Police Department.
It first appears parked presumably atop the roof of the New York Police Department head quarters. George Stacy alongside another cop/pilot climb inside in a rush to get across the city and stop the Lizard, before entering the vehicle he says "I want that spider guy off the streets." Talking to fellow police officers giving them the order to stop Spider-Man if they cross paths, which they do. When Spider-Man is seen making his way to Oscorp in order to use the reptilian antidote. When he is web swinging past the police force he shot at multiple times with taser blasters and managesto dodgethem until he turnsa corner and blinded by the spotlight given off by the NYPD helicopter which shoots a taser blast which successfully hits it target. Multiple cops including Captain George Stacy drop from the helicopter on ropes to arrest him. It is presumed later in the film after George lets Spidey go ahead that he uses the helicopter to make his way to the roof of the Oscorp tower.
When free-roaming around New York you can stop crimes, one of them is called a police deadlock which is a shoot out between a mob and the police, when Spider-Man goes to the location on the map he must web-rushonto an NYPD chopper for the event to begin, some shoot-outs take place on roof tops of buildings under construction where your starting position is sticking onto the chopper. This also repeated in "The Amazing Spider-Man 2 (videogame)".