The standard definition of Money supply in Economics is the amount of money in the economy.
Now differences arise in the way the money supply is calculated based on what components are included or excluded. The measures of money supply range from M0 which refers to the most narrow measure to M3 which denotes the broadest measure. M0 usually accounts only for the notes and coins in circulation in the economy and those deposited in banks. As we move to a broader definition, other instruments like demand deposits, traveler's checks, time deposits, money market instruments, etc. are also included.
Different measures allow a varying view of monetary resources present in the economy. As money supply is used to decide many important monetary factors like the interest rates, the amount that banks have to maintain as reserves, etc. it is essential to choose the appropriate measure for money supply.
The term money supply is used two related or similar variables describing the sate of economic condition of an economy or a country. These two different variables are often represented as M1 and M2.
M1 is a narrowly defined variables as compared to M2. It refers to the total supply of total coins, paper currency, and deposits in all demand or checking accounts in banks. Coins and note in bank vaults and therefore not in circulation are not included in M1. This represents the money that is used for facilitating the commercial transactions in the economy.
M2 is a more broadly defined variable. It includes all the items included in M1, plus some additional items. These are some liquid assets which are not as liquid as the assets in M1, but still play a part in facilitating economic transactions as these can be converted in the form of M1 assets quickly and at marginal cost. These include saving accounts, small time deposits and retail money market mutual funds. Also these are safe form of assets.
We use two different measures for money supply because the narrow money (M1) can be used for all type of transactions. Whereas the additional components of broad money (M2) can be used only for some kinds of transactions. For example we cannot use then for paying for the grocery we buy in a store.
Some economies also define other measures of money supply. For example M0 includes only coins and notes, and MB includes M0 plus Federal Reserve Bank Credit.