1: The Function of Money
Money is unnecessary in any society in which there is no free exchange of goods. An individual, producing for his own consumption, has no need of it. Neither does a household in which produces what it needs and consumers all it produces. The same can be scaled to an isolated village or a socialist nation in which all goods produced are claimed by the state and reallocated.
As such, the existence of money is the result of an economy based on the division of labor in which there is a notion of ownership of first-order goods (items consumed) as well as second-order goods (those which are required to produce first-order goods). In such a society, there is no centralized control of production.
In effect, production ins anarchistic: the decision of what to produce, in what quantity, and when is not subject to central control; such decisions are made by the owners of the means of production. However, balance is archived in the marketplace, as producers seek to maximize their value by producing goods in response to the abundance or dearth of need in the marketplace.
The Origin of Money
Money is a tool of indirect exchange.
In a direct exchange, one quantity of goods is traded for another. This is suitable when there are two individuals who are each interested in obtaining some quantity of the others' product and are willing to negotiate a trade for their own product.
When there are more than two parties, and more than two types of good in a market, it is theoretically possible to negotiate a direct exchange of goods in which all parties are satisfied, but requires such a level of effort to coordinate that commerce is more likely to be discomfited.
As such, indirect exchange becomes preferable: all parties price their goods in exchange against a single good, which performs the function of money. In the current (industrial) age, there are a plethora of goods and parties, and it is no longer feasible to engage in direct exchange.
The payment of wages is another matter that requires indirect exchange: while it was once desirable for a worker to receive wages-in-kind (a farm laborer receives a share of the crop at harvest), labor is better served by accepting incremental wages in money in lieu of working for long periods of time without compensation until the product of his labor becomes consumable.
(EN: The author doesn't go into this, but it stands to reason that labor for wages can be seen as receiving an advance of the future value of the goods he produces, and the risk that the goods will not be sold for the predicted price is born entirely by his employer.)
The existence of indirect exchange also results in the desire for an individual to produce goods that he does not wish to consume. That is, he may engage in the production of goods for sole purpose of serving the needs of other parties, who will consume him, and himself be rewarded for his effort by payment in a medium that can be exchanged to goods he actually desires. This is possible, but not facilitated, in a system of direct exchange.
It also stands to note that not all goods are equally marketable. Some have a "limited and occasional" demand (e.g., there is little demand for firewood in the summer, or medicine when a person is not sick). Historically, the goods for which there was constant and substantial demand became the first media of common exchange - that is, they became money.
It's also noted that precious metals were often chosen as money for a number of reasons: they were not perishable, had a high value-to-mass ratio, were not consumed by use, etc.
This is not to say that they are the only commodities suitable for use as money, as history has shown a myriad of goods being used as money. Neither is it to say that there would be only one commodity in use at any given time - it is possible, though somewhat problematic, to have several "monies" simultaneously employed as common media of exchange.
Secondary Functions of Money
Aside of serving as a medium of exchange, money has the function of distributing wealth over time. Provided the medium of exchange is, itself, durable, money grants the holder the ability to withhold value from the market to trade at a later date.
Money also facilitates credit transactions - in essence, an individual can not only withhold goods from the marketplace to trade at a later time, but he can also arrange to trade at the present time based on the value of goods that he will produce in the future.
The existence of money is thus prerequisite to both banking and credit.
Money also facilitates the transmission of wealth across distances, provide that the commodity that serves as money in one location also serves as money in another.
For example, a farmer can sell his acreage in Europe for money, then use that money to obtain a new plot of land in America two years later. In effect, he has traded one plot of land for another, but by means of an indirect exchange that has spanned both distance and time.
The use of money as a common medium also separates an exchange, such that the sale of one good and the purchase of another become independent transactions.
It would, however, be an error to presume that the secondary values of money supercede its primary value as a medium of common exchange. Value does not exist independent on the physical goods that money represents.