Money is a good that acts as a medium of exchange in transactions. Classically it is said that money acts as a unit of account, a store of value, and a medium of exchange. Most authors find that the first two are nonessential properties that follow from the third. In fact, other goods are often better than money at being inter-temporal stores of value, since most monies degrade in value over time through inflation or the overthrow of governments.
What Is Money? It Is More Than Pieces of Paper.
So money isn't just pieces of paper. It's a medium of exchange that facilitates trade. Suppose I have a Wayne Gretzky hockey card that I'd like to exchange for a new pair of shoes. Without the use of money, I have to find a person, or combination of people who have an extra pair of shoes to give up, and just happen to be looking for a Wayne Gretzky hockey card. Quite obviously, this would be quite difficult. This is known as the double coincidence of wants problem:
he double coincidence is the situation where the supplier of good A wants good B and the supplier of good B wants good A. The point is that the institution of money gives us a more flexible approach to trade than barter, which has the double coincidence of wants problem. Also known as dual coincidence of wants.
Since money is a recognized medium of exchange, I do not have to find someone who has a pair of new shoes and is looking for a Wayne Gretzky hockey card.
I just need to find someone who is looking for a Gretzky card who is willing to pay enough money so I can get a new pair at Footlocker. This is a far easier problem, and thus our lives are a lot easier, and our economy more efficient, with the existence of money.
What Is Money And How Is It Measured?
As for what constitutes money and what does not, the article How much is the per capita money supply in the U.S.?
gives the following definition, provided by The Federal Reserve Bank of New York