A central bank is responsible for
the stability of a country's currency and it's supply. It does so by controlling
interest rates, conducting open market operations by buying bonds and setting
the required reserve ratio for banks. A central bank also acts as a borrower
for banks as a final option. Governments on some countries have direct control
of their central banks allowing them to set their currency at a rate they desire
but a majority of the central banks are independent keeping political interests
at bay.
Central banks assume whether their country uses fiat currency, currency union,
gold-backed currency or a currency board. Most currencies today are not backed
up by anything so that "promise to pay" is basic trust that the currency
they're holding could be exchanged to the same currency which is worth the same
or a foreign currency carrying the same value. A central bank is also responsible
for issuing out a standard form of currency and can literally print out money
to back it's liabilities.