What is a Executive Order?

As with pardons, there have been a flurry of these on the national level in the past two days.

Unlike pardons, this power is not intended to check the powers of the other two branches. Instead it clarifies and narrows the power of the executive - specifically the president. It is to carry our what Congress tells it to do. The president cannot rule arbitrality, with discretion - or at least they are limits to the office's discretion.

Also unlike pardons, there is no specific mention of executive orders in the U.S. Constitution, but it is based on the take care clause in Article 2, Section 3 of the U.S. Constitution: 

He shall from time to time give to the Congress information of the state of the Union, and recommend to their consideration such measures as he shall judge necessary and expedient; he may, on extraordinary occasions, convene both Houses, or either of them, and in case of disagreement between them, with respect to the time of adjournment, he may adjourn them to such time as he shall think proper; he may receive ambassadors, and other public ministers; he shall take care that the laws be faithfully executed, and shall commission all the officers of the United States.

The requirement is also contained in the presidential oath which can be found in Article 2, Section 1, Clause 7:

Before he enter on the execution of his office, he shall take the following oath or affirmation:

"I do solemnly swear (or affirm) that I will faithfully execute the office of the President of the United States, and will to the best of my ability, preserve, protect and defend the Constitution of the United States."

For more: 

- Wikipedia.

- Federal Register.

- American Presidency Project.

- White House: Presidential Actions.

- White House: Initial Rescissions of Harmful Executive Orders and Actions.