Executive Order Law & Legal Definition. An executive order is an order issued by the President of the U.S, the head of the executive branch of the federal government. This term also refers to an order issued by a governor of a state. An executive order can also be called a decree or orders-in-council.xecutive Order Law & Legal Definition. An executive order is an order issued by the President of the U.S, the head of the executive branch of the federal government. This term also refers to an order issued by a governor of a state. An executive order can also be called a decree or orders-in-council.