What is Federal Reserve Bank?

Legal Definition
A Federal Reserve Bank is a regional bank of the Federal Reserve System, the central banking system of the United States. There are twelve in total, one for each of the twelve Federal Reserve Districts that were created by the Federal Reserve Act of 1913. The banks are jointly responsible for implementing the monetary policy set forth by the Federal Open Market Committee, and are divided as follows:

Some banks also possess branches, with the whole system being headquartered at the Eccles Building in Washington, D.C.
-- Wikipedia
Legal Definition
The 12 BANKS in the US FEDERAL RESERVE SYSTEM that are responsible for providing CENTRAL BANK services to member banks, lending via the DISCOUNT WINDOW, monitoring the activities of banks operating within their jurisdictions, and assisting in the formulation of MONETARY POLICY via the FEDERAL OPEN MARKETS COMMITTEE.