A gift circle (not to be confused with a giving circle, or the scam known as a gifting circle) is a group activity where participants sit in a circle, and (after a quick introductory round) follow three rounds:
In round 1, one participant expresses a need or desire he or she has. For example: a need for a toaster-oven, a need for help with math coursework, a desire to meet a potential romantic partner, etc. Then, whoever in the circle that might be able to help satisfy this needs says so, and gives his contact info (on pieces of paper) to the person that asked for help, so that they can later connect to fulfil the request. The turn then moves to the next person who expressed a need, and so on.
In round 2, one participant presents something that they can offer to others. It can be a physical object they no longer need, or a certain kind of help they can provide (e.g. help with fixing electronic devices), or a place they can offer for free use at certain times. Then, whoever in the circle can benefit from this offer says so, and gives his contact info to the person offering. The turn then moves to the next person who offers something, and so on.
In round 3, whoever wants can share success stories from previous giving circles from which he benefited. This helps to deepen the participants’ understanding of the power of a giving circle, and they are often surprised to hear how beneficial this activity can be.