Why do they call New York City the big apple??Why 'apple'?

Answer 1

The "Big Apple" is a nickname or alternate toponym for New York City.
Its popularity since the 1970s is due to a promotional campaign by the New York Convention and Visitor's Bureau.
Its earlier origins are less clear.
Further reading at:
http://en.wikipedia.org/wiki/Big_apple

Answer 2

When and how did New York City come to be called "The Big
Apple'?"

This is by far the most frequently asked question—and the
most hotly debated—to reach our New York History Hotline.

There are actually several answers (nothing about New York
City is simple, after all). All are explained below, with the last
word going, appropriately enough, to SNYCH’s own Joe Zito,
one of this burg’s finest purveyors of high-quality urban history.
A veteran both of New York City’s inimitable press corps and its
police department, Joe—happily for us—is able to provide
authoritative first-hand testimony on this topic. Read on!

Various accounts have traced the “Big Apple” expression to
Depression-Era sidewalk apple vendors, a Harlem night
club, and a popular 1930s dance known as the “Big Apple.”
One fanciful version even links the name with a notorious
19th-century procuress!

In fact, it was the jazz musicians of the 1930s and ‘40s who put
the phrase into more or less general circulation. If a jazzman
circa 1940 told you he had a gig in the “Big Apple,” you knew
he had an engagement to play in the most coveted venue of all,
Manhattan, where the audience was the biggest, hippest, and
most appreciative in the country.

Answer 3

Apple starts with A, and A is the first and the most important letter of the Alphabet, and NY is like the apple for the States!

Answer 4

http://gonyc.about.com/cs/atozinde1/a/bigapple.htm