Open market operations, or money market operations, are a central bank's sales and purchases of government bonds. They are usually carried out to keep the market in line with the target interest rate.
Open market operations may also directly target control of growth in the money supply, but this is rare. Most central banks directly target interest rates, and these are adjusted to meet inflation targets.
Another objective on open market operations is to ensure the liquidity of the banking system, so there is an element of short term control of the money supply. The short term liquidity of individual banks is ensured by central bank lending, such as discount window facilities.
Open market operations are the purchase and sale of government bonds and bills, and repos on them. The element of the money supply influenced by this is the narrow monetary base. The effect broad money depends on the money multiplier.
Detailed descriptions of how open market operations work are available from the Bank of England, the Federal Reserve Board and the European Central Bank.
When open market operations are carried with the intention of injecting money into the economy to stimulate it out of a recession, or just in order to finance government spending by buying an oversupply of government debt, this is called quantitative easing or printing money.