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.

The term was first popularized by New York sportswriter John J. Fitz Gerald, who wrote for the New York Morning Telegraph. Fitz Gerald first used the term in a column on 3 May 1921:

J. P. Smith, with Tippity Witchet and others of the L. T. Bauer string, is scheduled to start for “the big apple” to-morrow after a most prosperous Spring campaign at Bowie and Havre de Grace.