What is a central bank?
The institution behind a currency: it sets policy rates, targets price stability, and banks the banks.
A central bank is the institution standing behind a currency, and its published explainers describe four jobs that come with that position: it sets the policy interest rate that ripples through every loan and savings account in the economy, it targets stable prices rather than letting inflation run wherever it wants, it is the only body allowed to issue the physical and electronic money that currency is made of, and it lends to commercial banks when they run short, earning it the label “bank of banks”. No other institution holds all four roles at once.
What it is not
A central bank does not open current accounts or issue debit cards to the public — that is what commercial banks do, and you cannot walk in and deposit your salary. It is also not simply an arm of government: most central banks are deliberately structured with legal independence from elected officials, on the theory that interest-rate decisions work better when they are insulated from short-term political pressure, though how much independence any single central bank has in practice is a matter of ongoing debate among economists.
The one you live under
Every currency has exactly one central bank behind it, and which one governs your mortgage, savings rate and inflation outlook depends entirely on which currency you hold. The euro area’s is the European Central Bank, covering every country that has adopted the euro. Countries with their own currency have their own central bank instead — the mechanism is the same everywhere, only the name and the currency change.