The Federal Reserve is a quasi-governmental agency chartered by Congress, with no oversight or accountability, and run by representatives from the largest financial institutions. It is a cartel of nominally American bankers. Other than the presidential appointment of the Fed Chairman, the governors of the Federal Reserve are not democratically accountable to the American people. The Federal Reserve operates in nearly total secrecy and inexplicably is not subject to the Freedom of Information Act.
It's purported mission is to balance the competing and often inversely related phenomena of inflation rates and employment rates.
The Federal Reserve controls the interests rates that banks charge each other to borrow money from one another to meet their fractional reserve requirements. The Federal Reserve is also the lender of first/last resort when a banking crisis occurs.
In sum, the Federal Reserve is nominally a public agency but substantively a private cartel of bankers.