Wordorigins.org

This name for New York City was originally horse-racing slang that made its way into the vernacular. The metaphor is that New York City is a succulent and sweet prize to be had for those who are successful in racing or any field of endeavor.

Big apple was commonly used in the late-19th century to refer to the winnings of a wager. This use appears as early as the August 1847 issue of The American Farmer:

Try it once and we’ll bet you a big apple that you do it every year thereafter for the balance of your life.