The executive hierarchy
The executive branch is a pyramid: the President at the top, millions of civil servants at the base, and four recognizable layers in between.
The Executive Office of the President
The President's own staff and policy councils, the White House Office, the Office of Management and Budget, the National Security Council, and others. These are closest to the President and serve entirely at the President's pleasure.
The Cabinet departments
The fifteen great departments, State, Treasury, Defense, Justice, and the rest, each led by a Senate-confirmed Secretary (the Attorney General at Justice). They carry out most of the federal government's day-to-day work and answer directly to the President.
Independent agencies and commissions
Bodies Congress placed outside the departments. Some, like the EPA or NASA, are led at the President's pleasure; others, like the SEC, FTC, or FCC, are run by for-cause-protected commissions designed to operate at arm's length from the White House.
Government corporations
Business-like federal entities that earn revenue and are run by boards rather than a single head, the Postal Service, the FDIC, Amtrak, the Tennessee Valley Authority. They blend public mission with commercial operation.