The basic definition of a central bank is that it A) controls the money supply of a country and B) control the country's monetary policy. The central bank often also acts as a bank that lends to the other banks and as a regulator. However, it is a central bank's monetary policy functions that are most important.
A good example of this is the Federal Reserve, which is the central bank of the United States. The Fed is responsible for monetary policy by the fact that it does such things as setting the interest rates that it charges when it lends to other banks. The Fed also controls the money supply by buying and selling government securities. The Fed has recently announced that it will increase the US money supply by buying up around $600 billion in US government securities.