In this speech, President Clinton says that the United States plays a leadership role in the world.  He sees the US as a leader in world affairs.  We can see this in at least two places in this relatively short speech.  First, Clinton says that

America has been a force for peace and prosperity in every corner of the globe.

By saying this, Clinton implies that the US is a leader in making the world a better place.

Later, Clinton says that

People all around the world look to America to be a force for peace and prosperity, freedom and security.

Clinton argues that the world is becoming a much more interconnected place.  He argues that this process of globalization means that the US can and must get involved in places all over the world. 

In short, Clinton believes that the US is and should be a leader that works to make the world more peaceful and more prosperous.