Definition of New York back raise
A New York back raise is a play that you prepare when you know your opponents well. In short, it's a preflop call, anticipating a raise (squeeze) from an opponent and then re-raise (back-raise) in turn. Let's see an example. A player opens in UTG position. A player in MP position calls. You are on the button with AA. Here you could make a 3bet, but you would look very (too?) strong. And you know the player in the big blind position; he likes to squeeze. So you call with your aces on the button waiting for a squeeze. When the squeeze happens, you can make your back raise.
A New York back raise; perfect for mixing your game
In the situation described above, even if your opponent doesn't squeeze, you are still in position with aces, which can't be a bad thing. Many players will instantly 3bet with Aces on the button. But if you always make this play with your aces, when you call, your range is capped, you can no longer have AA and KK. That's why calling to entice your opponents to make squeezes is a good idea to vary your playing style.