Zines are self-published non-commercial magazines, usually created by a single producer and reproduced on a small scale. They are accessible, easy to make and carry the sense of being a unique object--a gift passed from creator to reader. Zinefests are independent community-supported events that provide a space to share zine culture with new folks as well as meet and spend time with other zine makers. In addition to opportunities to trade or sell zines, zinefests often feature workshops on do-it-yourself skills or topics, readings and art shows, and other fun events. They are usually great for all ages and there is probably one near you.
Zine World is one resource to help find zinefests (and other zine and small press activity):http://www.undergroundpress.org/upcoming-events/