Nachos originated in the city of Piedras Negras, Coahuila, Mexico, just over the border from Eagle Pass, Texas. In 1943, the wives of U.S. soldiers stationed at Fort Duncan in nearby Eagle Pass were in Piedras Negras on a shopping trip, and arrived at the restaurant after it had already closed for the day. The maître d'hôtel, Ignacio "Nacho" Anaya, invented a new snack for them with what little he had available in the kitchen: tortillas and cheese. Anaya cut the tortillas into triangles, fried them, added shredded cheddar cheese, quickly heated them, added sliced pickled jalapeño peppers, and served them.

When asked what the dish was called, he answered, "Nacho's especiales". As word of the dish traveled, the apostrophe was lost, and Nacho's "specials" became "special nachos".

Source: Nachos - Wikipedia