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:
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Try it once and we’ll bet you a big apple that you do it every year thereafter for the balance of your life.
Copyright 1997-2013, by David Wilton