By the Constitution, the Executive Department is established to grant powers and impose duties upon the Office of the President.
The powers granted to the Office of the President includes the title of Commander in Chief, thereby making the president the civilian and supreme leader of the armed forces. The president is given the power to grant reprieves and pardons for offenses against the United States, fill Senate vacancies, create Executive Departments (cabinet positions), conclude treaties, and appoint ambassadors and Supreme Court Judges and other "public ministers and councils."
And that's all the power the Office of the President is supposed to have.
For duties, the president is required to deliver an annual message to Congress (State of the Union Address), receive, not receive, or deport ambassadors of foreign countries, commission officers in the armed forces, and finally, and most importantly, to execute the law.