The 1920s were prosperous (for many, but not all, Americans) largely because of the fact that America had been modernizing for some time. By the beginning of the decade, the American economy had gotten to the point where it could make a lot of goods for relatively low prices. This had been accomplished through such things as Henry Ford's assembly line system. It had also happened because companies had learned how to organize and run themselves in a more efficient and professional manner.
The 1920s were also a time of laissez-faire government. The government did not try to regulate business much, thus helping it to grow.
Finally, there was a boom in consumer demand. This came about partly because of things like advertising and the start of really widespread buying on credit. It also happened simply because people came to be more centered on having fun and having material goods.
All of these things contributed to the prosperity enjoyed by many Americans for most of this decade.