Gift economy is a system based around getting people what they need (and want), without the use of money. Instead of a bartering system, where 10 eggs could buy you a kilo of flour, the idea is to give freely to everyone and anyone, and others will do the same for you, so that no one is left out. When and if you need something, just ask, and it will be provided. In turn, you give what you can to the next person who needs it. No money is exchanged, but the gift of goods flows to everybody.
Just like anarchic and consensus decision making systems, gift economies work best when people can see their own individual part in relationship to the whole. For instance, people need to see what they're needs are AS WELL AS what they have to offer and what other people's needs are. Without a grander view of needs/wants outside of self and friends and family, people tend to be a little more selfish. Creating this larger view also allows people to gift in accordance to what they have to offer. For example, someone who has lots of material wealth can gift any number of goods, whereas someone who has very little material wealth may have a service to offer. Value in a gift economy is not based on a dollar system, but rather in some combination of time, intention, community betterment, and perhaps environmental sensitivity.
Best used in a big community, with a lot of people. And of course, there's always the 'drain-bows' who bring nothing and get everything, but they're generally few and far between. Again, however, as more people become aware of their relationship to the whole, the less drainbows there will be.
Hospitality exchange networks such as BeWelcome are a form of gift economy.