Turning left from a red light a split second before it turns green, in order to beat the traffic on the other side of the intersection.
Your sitting at an intersection with a stoplight and it's red. There is someone on the opposite side of the intersection waiting for it to turn green as well. When you see the other light just turned red, you gun it and turn left before the other person has a chance to see the light turned green and goes. This is a New York Left.