What is money?

First, we try to define medium of exchange. Let us travel to a village right before the time money existed. Specialization has previously occurred, due to it's higher productivity becoming apparent to the villagers. Each person trades the excess of what they produce for things they don't produce. Sam is the new cobbler in our village, he makes and repairs shoes. He repairs peoples' shoes, and they repay him with vegetables, from the gardener; eggs, from the chicken farmer; clothes from the seamstress; etc. Now, let's say, Sam is allergic to eggs. He is unwilling to accept eggs for work performed, because he has no value for eggs. Sally, the chicken farmer, needs new shoes, but has no means of obtaining the nice, dry ones Sam makes. But suppose, Sally had an idea. She went to the wheat farmer, and traded eggs for wheat. Now Sally of course does this every week, trading eggs with Joe for wheat in return. But this time, she trades twice as many eggs, to get a double ration of wheat. Sally drops off her normal ration at her house, and takes the extra ration to Sam the cobbler. She offers it in trade for new shoes. Sam likes wheat, so accepts the trade. In our simple little barter village, this is the first instance of a commodity being used for something other than consumption. The commodity has acquired the characteristic of indirect exchange.
Now let us suppose Juan noticed that Sally traded wheat to the cobbler. Now, he grows rhubarb, which Sam hates, so poor Juan has been barefoot since Sam came to town. Juan then races over to Joes to trade his rhubarb for wheat, to get himself some shoes. Wheat has begun to take on the characteristic of a medium of exchange. The problem with barter is you must have a dual coincidence of desire. Both parties must want what the other has, and have what thee other wants. But a medium of exchange, since it is useful beyond immediate consumption, eliminates the necessity of a duality: as long as one party has a medium of exchange, then the trade can be executed.
So, as times passes, varios commodities may be used for indirect exchange, according to the preferences of the individuals at the specific time. This produces uncertainity, which humans try to eliminate. One commodity, perhaps jewelry or untoolable but workable rare metals, became commonly accepted, and tradition would follow. Now the medium of exchange is worth more than just the barter value. Now it is money.