What is the general nature of the presidents job? Not including duties and responsibilities. Ex. president is the leader of the free world?

United States Constitution.
Article II.

It says nothing about being leader of the free world.

The President of the US runs most of the government, making sure that government services operate effectively and efficiently. He is also commander in chief of the US military. Since the US is arguably the most important and influential country, he plays a large role in world affairs, generally working toward greater peace and stability.