M2 is defined as a “measure of money supply that includes checking deposits (M1) cash as well as (what is colloquially referred to as) near money”.
“Near money" in the case of M2 includes mutual funds available in the money markets, also savings deposits and other types of time deposits, which are less liquid than cash and as such are not suitable as cash-on-hand exchange mediums but may however be quickly converted into either cash or checking deposits.
The American Fed or Federal Reserve System classifies M2 as “M1 plus savings deposits, small-denomination time deposits (those issued in amounts of less than $100,000), and retail money market mutual fund shares.”
M2 includes close substitutes for M1
M2 actually characterize not just M1 but also "close substitutes" for M1 and as such is a far wider classification of money as compared to M1.
M2 as economic indicator
M2 is by and large a very important economic indicator and is quite frequently used to forecast inflationary trends. In fact M2 forecasts recessionary trends to such an extent that it is widely used as a leading indicator of a nations’ economy.
M2 as opposed to M3
M2 is quite different from M3 in the sense that M3 not only includes both M1 as well as M2, but also large term deposits, institutional money market funds (some of which may be held by the mutual fund industry) along with other larger liquid assets. Typically they can’t be converted into cash reserves immediately and are therefore referred to as near money due to their perceived lack of liquidity in the money supply chain.
M3 is usually utilized by economists to create varying estimates of the total money supply available within the economic system of a country. It is also used by various governments to not only control inflation but also direct fiscal and monetary policies. This way it also helps control runaway inflation over both long as well as medium terms.
However, the American central bank has effectively stopped tracking M3 since the past decade or so.