Economists since the times of Adam Smith (1723-1790), looking at non-specific pre-modern societies as examples, have used the inefficiency of barter to explain the emergence of money, of "the" economy, and hence of the discipline of economics itself. However, ethnographic studies have shown that no present or past society has used barter without any other medium of exchange or measurement, nor have anthropologists found evidence that money emerged from barter, instead finding that gift-giving (credit extended on a personal basis with an inter-personal balance maintained over the long term) was the most usual means of exchange of goods and services.
In trade, barter (derived from baretor) is a system of exchange where participants in a transaction directly exchange goods or services for other goods or services without using a medium of exchange, such as money. Economists distinguish barter from gift economies in many ways; barter, for example, features immediate reciprocal exchange, not delayed in time. Barter usually takes place on a bilateral basis, but may be multilateral (i.e., mediated through a trade exchange). In most developed countries, barter usually only exists parallel to monetary systems to a very limited extent. Market actors use barter as a replacement for money as the method of exchange in times of monetary crisis, such as when currency becomes unstable (e.g., hyperinflation or a deflationary spiral) or simply unavailable for conducting commerce.
It’s hard to answer that without actually seeing a modern gift economy in action. Luckily, modern gift economies actually do exist. On a small scale, they exist among friends, who might lend each other a vacuum or a cup of flour. There’s even an example of a gift economy on a much larger scale, albeit one that’s not always in operation: The Rainbow Gathering, an annual festival in which about 10,000 people gather for a month in the woods (it rotates among various national forests around the country each year) and agree not to bring any money. Groups of attendees set up “kitchens,” in which they prepare and serve food for thousands of people every day, all for free. Classical economists might guess that people would take advantage of such a system, but, sure enough, everyone is fed, and the people who don’t cook play music, set up trails, teach classes, gather firewood, and perform in plays, among other things.