The money supply is the amount of money in an economy. This is superficially straightforward but is complicated by the difficulty of defining what is meant by money.
The simplest possible definition is the actual amount of bank notes and coins in circulation. The problem with this simple definition is that most money exists as bank deposits and other such obligations rather than in physical form.
Measures of money supply
Even the narrowest of the definitions that are actually useful, M0, is broader than physical notes and coins as it includes banks' deposits with the central bank.
The next narrowest measures of money supply are M1 and M2. These add various types of deposits by the private sector with banks and other financial institutions. These are still regarded as narrow measures. They are sometimes referred to as referred to as narrow money.
Narrow money measures aim to measure the money supply that is actually held for use in transactions. Broad measures also include money that may be held as a store of wealth. Divisia aggregates weight different types of money, giving a higher weight to those likely to be used for transactions.
There are various variations on these basic types and the exact definitions vary from country to country. The exact definitions are revised from time to time by the Bank of England (or the appropriate central bank).
Control of money supply
In practice monetary policy targets interest rates, rather than directly targeting money supply. In most countries control of inflation is the policy objective (i.e. interest rates are set to keep inflation at desired levels). See M0, open market operations and interest rates.
Where the policy target is to stimulate the economy or o fund government spending, the increase in the money supply is usually described as printing money (or, euphemistically, quantitative easing).