The federal government needs an administration to carry out its several duties outlined in the Constitution.
The President, for example, is responsible for the execution and enforcement of the laws created by the Legislative Branch. In order to accomplish this task, one of the bodies that the executive is the Cabinet, which consist of the Vice President and the heads of 15 executive departments, who advise him. These fifteen executive department's goal is to carry out the day-to-day administration of the federal government regarding the areas that concern them, whether it's transportation, homeland security, education, energy, agriculture, defense, commerce, health and human services, housing and urban development, interior, labor, state, transportation, treasury, veterans affairs or attorney general.
Similarly, Congress needs an administration to fulfill its legal powers of regulating commerce within the states, providing and maintaining a navy, establishing post offices, etc. And although the Constitution does not specifically states that the Congress should establish an administration, it does holds The Necessary and Proper Clause in Section 8, which states the following:
Congress shall have power to (...) To make all laws which shall be necessary and proper for carrying into execution the foregoing powers, and all other powers vested by this Constitution in the government of the United States, or in any department or officer thereof.
