Central banks have multiple roles that vary between countries but maintaining financial stability is common to all of them. That means keeping inflation in check by setting interest rates, also called their interest rate policy. The most influential central bank is the US Federal Reserve (the Fed) where rate policy is set by the Federal Open Market Committee (FOMC). The minutes of their committee meetings are published and pored over by analysts all over the world because US interest rates are a prime mover of all global markets.
The mandate for the Fed is two-fold: maximizing employment and stabilizing prices (inflation). Next most influential is the European Central Bank whose mandate is to maintain inflation at or just below 2%. In the UK we have the Bank of England (BoE) and Japan has the Bank of Japan (BoJ). Several central banks also have a duty to regulate the banking system and to control the creation of physical currency.