What does the executive branch do with the law?
The constitutionally stated purpose of the executive branch, in the U.S. Constitution at Article II, is to make sure the laws of the United States of America are carried out and obeyed. Where Article II says, "The executive power shall be vested in a President of the United States," it means that there is one person who has the executive power in the U.S. How broad that power is has been debated and challenged since the Constitutional Convention in Philadelphia in 1787. In 1908, Woodrow Wilson wrote in Constitutional Government in the United States that the "President has the right, in law and conscience, to be as big a man as he can." While that does not infer the President is all powerful, it does show us that presidential power is immense. That power is not unchecked, however, due to the system of checks and balances as well as the separation of powers established in the Constitution.
Nonetheless, Article II, Section 2 of the Constitution does list specific powers and duties of the President, including Commander in Chief of the U.S.Military; the power to make treaties, executive agreements,* and compacts; appoint and receive ambassadors to or from other countries; and grant pardons and reprieves. Treaties require ratification by the Senate while executive agreements and compacts (like Lend Lease during WWII and trade agreements) do not. Nevertheless, agreements and compacts often have Congressional backing.
The President heads the executive branch but does not work alone. Presidential advisors include the Cabinet, which was defined in Article II, Section 2 of the Constitution, includes the Vice President and 15 other departments like State, Treasury, Defense, Justice, Agriculture, etc. Departments within the cabinet have been added over the last 229 years, and the last cabinet department to be created was the Department of Homeland Security. Other supporting entities that are not specifically named in the Constitution are the Executive Office of the President (like the National Security Council, Office of Management and Budget, etc.) the Senior Whitehouse Leadership (Chief of Staff and others), and many other advisory boards.
Execution of the laws of the land is a big job that cannot be handled by one person. It takes numerous advisors and departments to carry out the tasks of the executive branch of the United States Government and make sure the laws are carried out and obeyed. You can find out more about the advisors to the President here.
*Don't confuse executive agreements with executive orders. An executive agreement is an international agreement between the executive branch and a foreign government. Executive orders have the full force of law but do not require Congressional approval. For that reason, some people object to the number of times EOs are passed by presidents. The last 3 presidents have not used the executive order excessively -- Clinton 364, GW Bush 291, Obama 252. The record number of EOs was set by FDR with 3,721.