A white elephant gift exchange is an event where, generally, items that are unwanted are exchanged for gifts that are. Gifts that people bring are often opened in a randomized order in front of everyone. Later participants often have the ability to steal gifts that have been revealed in this manner or open a still unwrapped present.
In other circles, white elephants gift exchanges are also known as Yankee Swap, Gift Swap, Dirty Santa, and Naughty Santa.
The term white elephant comes from the idea that a white elephant, although nice, is not all that useful.
For more on the rules, check out our handy planning guide.