The term "Big Apple" is a nickname for New York City, and it's origins are unclear. One popular theory suggests that it comes from the expression "going to the big apple," which means going into town to sell goods or attend market. Another theory points towards the fact that in the 19th century, New York had a large number of horse-drawn carriages, and if one missed their stop, they would have to go around again - hence the term "going around the big apple."
Whatever its origins may be, today the phrase is synonymous with New York City, often used as a symbol for the city's vibrancy and energy.