A banker's bank is an institution that provides banking services to other banks, just as commercial banks provide services to individuals and businesses. This role is performed by the Central Bank.
As the banker's bank, the Central Bank:
Holds deposits (reserves) of commercial banks
Provides clearing and settlement services for interbank transactions
Lends to commercial banks, especially as a lender of last resort during liquidity crises
Sets reserve requirements that commercial banks must maintain
Supervises and regulates the operations of commercial banks
Commercial banks serve the general public, not other banks. Development banks provide long-term financing for specific sectors such as agriculture and industry. Mortgage banks specialize in providing loans for property purchases. None of these serve as the bank for other banks.
In Nigeria, for example, the Central Bank of Nigeria (CBN) performs this role for all commercial and merchant banks operating in the country.