The "Big Apple" is a nickname for New York City.
The first recorded usage was by Edward S. Martin in his 1909 book The Wayfarer in New York, who wrote (regarding New York) that the rest of the United States "inclines to think the big apple gets a disproportionate share of the national sap."
Used in the title of a column in the New York Morning Telegraph, "Around the Big Apple with John J. Fitz Gerald," which first appeared in 1924.
The term lost popularity in the 1950s, but was brought back into wide use after a 1970s promotional campaign by the New York Convention and Visitor's Bureau.