Discussion: What is a President?

A wide-ranging discussion loosely centered around the political role of the President of the United States.

Here are just a few motivating questions to keep in mind:
What does a President do?
Where does the President's power come from?
What are or ought to be the duties of the President?
How has the office of the Presidency evolved?

A related reading (not required) which we can point to for historical purposes are the Federalist Papers, specifically No. 67-77. Those should all be published online in full.
Example: Federalist No. 69 [https://founders.archives.gov/documents/Hamilton/01-04-02-0220]