The Supernatural fandom is the community of fans that formed around their common interest in the TV show.
The creative Supernatural fandom produces a range of material in response to and celebration of the show, including fanfiction, fanart, meta and fanvids. Other Supernatural fan communities engage in speculation, reviews, etc. rather than the more typical creative production forms listed above.
There are several online locations that Supernatural fans house their communities on, including sites like Television Without Pity, Livejournal, TV Guide Blogs, CW Lounge and the forums of various websites specific to the show and its actors.
See the Fandom category for the pages on the Super-wiki specific to fandom matters.
A History of Supernatural Fandom can be found at Super-Wiki's Fandom Chronicles.