What's a "fanzine", you ask?
Fanzines are important cultural artifacts that document the development and continuing life of particular social communities - in this case, fans of specific genre topics (i.e. science fiction). Fanzines were originally devoted to chronicling people's interest in literary science fiction, but over the course of the 20th (and into the 21st) Century they have been adopted as vehicles of personal and cultural expression by a number of new fan communities.
Science fiction fandom has been a vibrant subculture, with its own particular jargon, rituals, and relationships to mainstream culture, since at least the late 1920s. It emerged as a semi-organized community of like-minded individuals as a response to the rise of professional science fiction magazines. Hugo Gernsback published the first of these, Amazing Stories, in 1926, and fans responded with enthusiasm (sometimes critical enthusiasm) to the new stories by writing letters of comment to the magazine. Eventually, fans used these letters to begin making contact with each other; this led to the creation of both formal and informal fannish organizations, where SF fans - who often felt marginalized by the greater culture for their particular interests - could meet, socialize and talk about science fiction. The first fan-produced magazine, The Comet, was published in May 1930 and represented the start of a long and continuing tradition of science fiction fanzines.
Today fanzines (many of which have taken electronic form as e-zines) take on a number of forms. They can consist of - to name a few examples - essays, editorials, reviews, collections of letters, pieces of graphic art, or fan-written fiction that chronicles new or alternative adventures in the lives of fans' favorite characters and media universes.
Fan fiction ("fanfic") is a vibrant and popular subgenre of fanzine. Fan fiction consists of stories, artwork, poetry and songs that take place in a particular media universe (i.e. Star Trek, Star Wars), written by fans on a amateur basis rather than by either the universe's creator(s) or professional writers.