A socioeconomic construct in which your worth or social status is measured by how much you give away rather than how much you own. 

The OpenSource movement is an example of one of these; the main way to get social status is to give away some cool code. 

Some people misinterpret this as generosity.

(More accurate and/or insightful explanations invited.)
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Of course, giving useful gifts is a sure way to improving your reputation (Nobody doesn't like SantaClaus). Improving your reputation or social status translates to more economic opportunity. 
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Seems like a handy method of AddingValue to the economy/market/thingy.  In a situation where everyone can produce, only weirdos would stockpile their goods.  Its not like they're running out.  

When you create the illusion of scarcity, however, your constituents will not want to trade with each other as much.  The economy/market thingy becomes a ZeroSumGame with big scarey organizations at the top, and everyone trades with them out of fear.

BruceSterling describes a gift economy coordinated by AI and the internet, and how it clashes with traditional society, in a story called ManekiNeko, collected in his book 'A Good Old-Fashioned Future'. According to Christina Schulman, on Epiphyte Book Review (http://www.epiphyte.net/SF), ''"Maneki Neko" runs counter to every paranoid story ever written about computers taking over our lives. Computers have made people anonymous, but not impersonal. Even those who try to fight the system benefit from it. Trust the computer; the computer really is your friend.''
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To point out the obvious, wikis work in part through gift economy processes.

A GiftEconomy is also one way of GettingToPostScarcity, perhaps interwined with other things like a BasicIncome, LocalSubsistence, and ResourceBasedPlanning.