Who is the head of the Executive Department? What is his/her most important
job?

The President of the United States

The President of the United States is the head of the executive branch. The President gets help from the Vice President, department heads (called Cabinet members), and heads of independent agencies.

On the afternoon of april 30, 1789,george washington  stepped out onto the balcony of federal hall in lower manhattan to take the oath as the  first president of the united states.