Fanon is a term used to refer to "fan canon" (of which the term is a portmanteau). It applies to certain "facts" that may have been accepted as a truth by a large number of fans, and thus either replaces an established canonical fact in the minds of those fans, or fills a plot-hole. Frequently, these fanonical facts arise due to screen adaptations (esp. The Lord of the Rings (film series)).
Due to the nature of the work, much pseudo-scientific speculation is encouraged in order to explain motivations, facts, reactions and generally fill some gaps. This differs from proper fanon since such study does not invent new elements from scratch, but rather attempts to reveal how canon is. See also Tolkienology.
Fanon can also take the form of personal beliefs held by individuals. In this case, an individual may create an expansive backstory, possibly a fan fiction, which they accept as "true." These have less standing than even the fanon mentioned above, and thus are not included on Tolkien Gateway.