I like this diagram in particular.

It covers the main relationships/roles of a central bank:

1. it is a bankers' bank so we see the commercial and other banks interacting with the central bank.
2. it is the government's bank. Here we see the national government have accounts in the bank and it also goes to the central bank for funding. Central Banks purchase Treasury Bonds and Notes in particular to fund government expenditures in deficit scenarios.
3. it is the lender of last resort. For other banks and the government, they go to the central bank when they need emergency liquidity. This is particularly useful in times of temporary liquidity constraints.

Original Image found here: Speculative Numismatics | Festival work @ Memefest.