The National Basketball Association was founded on 6 June 1946, so it is now 67 years old. It was originally called the Basketball Association of America when it was founded in New York City, but changed its name to the National Basketball Association in 1949. This was because it had taken over another organizaton, the National Basketball League, which had formerly been a competitor.
Since this merger in 1949 the NBA has been the most important men's basketball league in North America, with players coming from all over the world to join it. The headquarters are still in New York although it also has offices in New Jersey. It is also connected to other organizations like the NBA Development League, which is the minor league organization, and the WNBA which is the women's professional league.
You can find out more about the NBA here.