"The Big Apple" is a phrase that has been used to describe the city of New York since the early 1920s. Several stories of the start of this phrase exist. They come from a variety of sources. All of them are sensible, but we will probably never be able to agree on its actual origin.
One version of the origins of "The Big Apple" was reported in a 1977 newspaper column called "The Straight Dope" written by Cecil Adams. He reported that the phrase got its start in show business circles. The quote was: "There are many apples on the tree, but only one 'Big Apple.'" This reference supposedly was made by jazz musicians comparing a show in New York City as the biggest opportunity of all.
It also may have been a reference to the apple vendors on the sidewalks of New York during the Depression. The "Big Apple" was also the name of a popular nightclub in Harlem. The Big Apple was also a jitterbug-style group dance that originated in the South. It became a huge hit at Harlem's Savoy Ballroom.