Why is a central bank described as the bank for banks?

1. A central bank lends money to banks that need it. 2. That is exactly the service an ordinary bank performs for its own customers, which is why the label fits. 3. The rate charged on this lending is the discount rate. 4. The public does not keep accounts there, so it is not a bank for banks in the sense of holding household savings. _Source: OpenStax Introduction to Business (CC BY 4.0), Ch 15 "Understanding Money and Financial Institutions", section 15.2 The Federal Reserve System_