It is base on the story...In the early 1920s, "apple" was used in reference to the many racing courses in and around New York City. Apple referred to the prizes being awarded for the races -- as these were important races, the rewards were substantial.
Based on the research of Barry Popik, the use of "Big Apple" to refer to New York City became clearer. Popik found that a writer for the New York Morning Telegraph, John Fitzgerald, referred to New York City's races "Around the Big Apple." It is rumored that Fitzgerald got the term from jockeys and trainers in New Orleans who aspired to race on New York City tracks, referring to the "Big Apple."
In the late 1920s and early 1930s, New York City's jazz musicians began referring to New York City as the "Big Apple." An old saying in show business was "There are many apples on the tree, but only one Big Apple." New York City being the premier place to perform was referred to as the Big Apple.