The Federal Reserve, also known as the Federal Reserve System, is effectively the central bank of the United States. Its nature is quite special; it cannot simply be categorized as a private institution or a government agency, but rather a hybrid.
The core management body, the Federal Reserve Board, is located in Washington, with 7 members responsible to Congress, which falls under the public sector. There are 12 regional Federal Reserve Banks located in major cities such as New York and Chicago; although they are ostensibly owned by member banks, they are strictly regulated by the Board.
The mission of the Federal Reserve is to maintain the stability of the U.S. economy, formulate and implement monetary policy, and oversee financial institutions, among other responsibilities. It is relatively independent in policy-making to avoid short-term political interference. However, it has also been accused of being the 'fourth branch' of power that manipulates the economy of the U.S. and even the world.