New York-style pizza dough is an offshoot of Neapolitan-style dough designed to be cooked in a slightly cooler-burning coal-fired (or as is more often the case in modern New York pizzerias, gas-fired) ovens. It's stretched out slightly thicker than a Neapolitan base, though on the scale of pizzas, it's still considered "thin crust."
The crust has to be sturdy enough, but—and this is important—just sturdy enough. Crunchy, tough, or cracker-like are not adjectives that can ever accurately describe a great New York pizza. The slice must crackle and give gently as you fold it, never crack or split. When bent slightly down the center (A.K.A. the "New York Fold"), it should cantilever out straight under its own support.