This is a good question. The United States is important in the world economy in several ways. Let me list a few.
First, the United States is still the largest economy in the world. For this reason, the world still depends on the United States to consume its products. Without this consumption, the world economy would suffer greatly.
Second, America leads the world in the finance sector. This is no small matter. Most of the world still is investing in our markets.
Third, nations are still buying United States debt. Part of the reason for this is because the United States is still one of the safer countries. Think of the EU and the problems its faces due to Greek, Italy and Portugal. You can say that there is a flight to safety.
Finally, the dollar is still the world's currency and equally as important oil is priced in dollars.
In short, the United States is the single most important economy in the world. In the past the United States lead growth. In the future, I will lead with China.