Trading goods and services without the use of money is called bartering. Early civilizations relied on this kind of exchange. Even cultures in modern society rely on it. Think of people in prison who commonly trade cigarettes for protection or extra food. For the most part, they don't have cash. So, like people in pre-currency economies, they work with what they have.
Although, as a general case, a ship unlucky in falling in with whales continues to cruise after them until she has barely sufficient provisions remaining to take her home, turning round then quietly and making the best of her way to her friends, yet there are instances when even this natural obstacle to the further prosecution of the voyage is overcome by headstrong captains, who, bartering the fruits of their hard-earned toils for a new supply of provisions in some of the ports of Chili or Peru, begin the voyage afresh with unabated zeal and perseverance.
If you've ever swapped one of your toys with a friend in return for one of their toys, you have bartered. Bartering is trading services or goods with another person when there is no money involved. This type of exchange was relied upon by early civilizations. There are even cultures within modern society who still rely on this type of exchange. Bartering has been around for a very long time, however, it's not necessarily something that an economy or society has relied solely on.
As Orlove noted, barter may occur in commercial economies, usually during periods of monetary crisis. During such a crisis, currency may be in short supply, or highly devalued through hyperinflation. In such cases, money ceases to be the universal medium of exchange or standard of value. Money may be in such short supply that it becomes an item of barter itself rather than the means of exchange. Barter may also occur when people cannot afford to keep money (as when hyperinflation quickly devalues it).
Bartering does have its limitations. Many bigger (i.e., chain) businesses will not entertain the idea and even smaller organizations may limit the amount of goods or services for which they will barter (i.e., they may not agree to a 100% barter arrangement and instead require that you make at least partial payment). But in an economic crunch, bartering can be a great way to get the goods and services you need without having to pull money out of your pocket.