A fanzine is a usually small-press publication catering to fans of a
 particular genre.  (As M. High pointed out, "furry" is more a *vehicle*
 than a *genre*, but that's a technicality.) There are several "furry
 fanzines" which publish an assortment of stories, artwork and sometimes
 articles submitted to the 'zine, such as "PawPrints" and "YARF!".

 Other publications that may pop up in "furry" discussion are APAs:  These
 are limited-circulation publications meant for a collection of
 artists/writers to share their work with *other* artists and writers. 
 Usually each contributor pays his share of the production costs depending
 upon how much of each "issue" consists of his work, and copies of the
 collected publication are only circulated among the contributors.
 Examples include "Rowrbrazzle" and "Furthest Northern Crew (FNC)".

 A variation on this is the APA'zine, which is an APA which accepts
 contributions only from members but which allows non-members to purchase
 copies.  Examples include "Huzzah!" and "Gallery".