According to the Merriam-Webster Dictionary, administration refers to the activities that are related to operating an organization such as a company or a school; the collection of individuals who run an organization; or the part of a government that is identifiable with that government's leader. The medical definition of administration refers to executing something directly or doling out medication. The word was first used in the 14th century.
In the United States of America, the people who work in the White House, including those who work in the Cabinet, the East Wing, the West Wing and the Executive Office of the President, are part of the government's administration. The president and vice president are the figureheads of the U.S. government's administration. There are many councils and offices that make up the Executive Office of the President, including the Council on Environmental Quality, the Office of National Drug Control Policy, the Domestic Policy Council, the Council of Economic Advisers, the Office of Intergovernmental Affairs, the Office of Urban Affairs and others. Additional advisory boards that are part of the administration of the U.S. government are the President's Management Advisory Board, the White House Council for Community Solutions, the President's Council on Jobs and Competitiveness and more.