Money is a term we all understand intuitively, but rarely stop to think about formally. What is "money"? Is it the dollar bill in your pocket? How about the dollars in your bank account? Is that money?
The dollars in your bank account are part of your assets, but they are not, directly, "money". Money is the dollar bills in your pocket. In theory, you can go to your bank and convert the dollars in your bank account in to money - dollars in your pocket. But that isn't ALWAYS true. Before automated teller machines, the bank had to be open. In the 1930's, a lot of banks failed, and there was no FDIC, or FSLIC, or NCUA, and when a bank failed, your asset - your deposit at the bank - suddenly became worthless. So the dollars in your bank account aren't really money. They are promises by the bank - and it's backers, the FDIC - to give you or your designees money on demand.
What's special about the dollar bills in your pocket? What makes those pieces of paper worth a dollar?
What makes them worth a dollar is our society's broad acceptance of them as dollars. And the ease and confidence with which you and I can 'validate' that the piece of paper is, in fact, a dollar and not a counterfeit.
In a pure barter society, there are two very real problems that money solves. First, your need for what I can offer you rarely coincides with my need for what you can offer me. If you sell coffee, and I sell computers, but don't drink coffee, how are we to trade? Even if I'm willing to accept your coffee, knowing that a lot of the people I trade with want it, how do I know that the coffee you're selling is the quality you say it is? Since I don't drink coffee, I don't know anything about how to evaluate coffee. You, being in the market for a computer, will have learned enough about what you want to be satisfied that what I'm offering meets your needs.
Money solves these two problems. You and I both know what a $20 bill looks and feels like. I don't have to take your coffee, or my other customer's products or services. I don't need to become qualified to evaluate their quality. And I don't have to take delivery of a year's worth of coffee in order to deliver to you a computer. You sell enough coffee to the whole town to collect enough $20 bills to trade me those $20 bills for the computer.