Open Market Operations are the means by which central banks control the liquidity of the national currency. This management of liquidity is used to achieve certain monetary targets. It is the basis for monetary policy.
The process entails the use of newly minted national currency to buy in the open market some financial asset, typically gold, foreign currency or government bonds. Alternatively it may involve the selling in the open market of a financial asset in order to redeem back national currency.
These operations affect the liquidity of the national currency. They increase or decrease the amount of national currency that is in circulation. This currency component of the money supply is known as M0. Stated differently M0 refers to the amount of cash (coins and banknotes) in circulation.
Under most inflation targeting monetary systems open market operations are used to achieve and maintain a target interest rate. This target interest rate is periodically reviewed. Under such a scheme inflation is typically defined and measured using a consumer price index.
Under a gold standard such open market operations would be used to achieve and maintain a target gold price. The goal would be to always keep the value of the currency near constant relative to gold.
Under a currency board such open market operations would be used to achieve and maintain a fixed exchange rate with some foreign currency.
Economist Robert Mundell has famously stated that when using open market operations it is only possible to pursue a single target at any given time. You can not use open market operations to target interest rates whilst being on a gold standard. Likewise if you are targeting interest rates then the price of gold will fluctuate.