Question

What are some roles that the president plays in the U.S. government?

Answer 1

The president does just that - he or she presides over the government and additionally is charged with running the executive branch. What few know any more is that the Founders deliberately made the presidency a weak office. They didn't want to give the president powers by which to become a dictator. The idea was that the man or woman holding it would fill the office with their strength of personality and character.
The president is also Commander-in-Chief. This was done for two reasons: No military will be effective if run by committee, and; the concept of civilian control of the military runs very deep here. That's why we don't have this-week's-general taking over in a coup, like South America.

The president must propose a budget for his agencies to spend as they execute Congress' wishes. He as well must deliver - how isn't specified but a speech is traditional - a state-of-the-union message yearly.