The money supply is all the money in a country at a given time. It's used in the equation velocity * money supply = real GDP * GDP deflator. Money supply is useful, then, for calculating inflation: if the money supply is growing and simultaneously stock market prices are on the up and up, with firms issuing equity and debt, prices will rise and interest rates charged by financial institutions will go up. The money supply separated into three different categories, with the numbers going higher as a broader spectrum of available monies is considered.

M1: Includes currency (defined as paper money and coins issued by the Federal Reserve1,) travelers' checks, demand deposits (common checking accounts), and other checkable deposits (being those released by non-commercial banks, such as Savings and Loans and credit unions.) The important difference between here and M2 is that the accounts gain no interest; holding onto a dollar or a checking account for five years will yield only the same amount of money as you started with, or, effectively less.
M2: All of M1, plus CDs, savings accounts, and other easily liquidated assets.
M3: M1, M2, plus $100K+ savings accounts and CDs held by private institutions. The $100K barrier, incidentally, is the upper limit of FDIC insurance.

1-In the European Union, the Euro is controlled by the European Central Bank (Banque centrale européenne, la.) Japan's is the Bank of Japan (or Nippon Ginko.) England's is the Bank of England. All mentioned have figures of the money supply; the US's M1 is around 1.4 trillion dollars.

Thanks to the Junior Achievement Economics textbook, of which I gleamed some info.