The reason that there are many measures of money is because money can be more or less liquid. It is important to know how much money is out there in the economy, but it is also important to break down that information so as to know how liquid the money is.
One of the major reasons that we need to know the size of the money supply is because the money supply has a major impact on how much economic activity can take place in an economy. However, not all forms of money will have the same impact on economic activity. The more liquid forms of money will have more of an impact than the less liquid forms. If we only measured money in one way (if we included M1, M2, and M3) then we would know how much total money was in the system, but we would not know how liquid it was. This would reduce the value of the information that we had.
Thus, we need to have different measures of money so as to really know how much money is available for relatively immediate use in economic activity.