By money I mean a medium of economic exchange, something that can easily be exchanged for most other things.
To illustrate, I will imagine that person A has item X and wants item Y, while person B has item Y and wants item X.
I first consider what people do in societies without money.
In barter, people exchange items. A gives X to B and B gives Y to A. This requires a “coincidence of wants”, which can be unlikely.
In a gift economy, people give items, and the recipients give other items back. Thus, A gives X to B, and B remembers A’s favor and returns it by giving Y to A. There is still a problem with a coincidence of wants, though a weaker one.
These two approaches do not scale very well, and that is why money was invented, and invented several times. Consider money item M and a merchant S. A sells X to S for money M and buys Y from S for M. Likewise, B sells Y to S for M and buys X from S for M. The two transactions are now decoupled and a coincidence of wants becomes unnecessary. Let us now see what sorts of money have been used.
The simplest is commodity money, some item traded at its non-monetary value. Numerous items have been used as commodity money, like various metals, various seashells, salt, cows, and cigarettes. The latter has been used by inmates of World-War-II concentration camps, among others.
However, commodity money, though often relatively portable, is often not portable enough. Thus the invention of representative money, some item traded at much more than its non-monetary value. Paper money is the most well-known example of this, and it originated as IOU’s for the likes of gold and silver. Coins may also serve as representative money, and a common type of it nowadays is entries in banks’ computer databases.
Representative money need not be IOU’s for commodity money. It can be fiat money, money decreed int existence (Latin “let (it) be made”, not the Italian car). A big problem with fiat money is that central banks can print large amounts of it or do similar things with its computerized equivalent, producing lots of inflation.
Such monetary fraud as counterfeiting and coinage debasing are essentially forms of fiat money, and some people consider all fiat money to be forms of monetary fraud. Such people often want to return to the gold standard, which is essentially reducing paper money to IOU’s for gold.
This raises a serious question about whether a large-scale, high-tech society can have no money. That was supposedly the case for the United Federation of Planets in the Star Trek universe, or at least for the Earth in it. But if a society does have money, it would be a great achievement if it avoided many of the economic and social pathologies associated with it.