Fanon is a so-called "fact" that a significant number of fans think is true, but for which there is no evidence in any official material. A piece of fanon usually becomes widespread due to having been discussed and picked up by other fans. Some fanon is based on misinterpretations of canonical events and some are simply stuff fans made up that makes sense. While fanon originates with fans rather than the official canon of the Ghostbusters universe, it sometimes becomes incorporated into the canon if the writers uses a retcon or otherwise establish the fans' interpretation in official fiction.
Misuse of the term has broadened the word's definition (among some) to include fan-characters and fan-fiction. The difference is that fan-fiction is an extension built upon canon, while fanon is an interpretation or explanation of existing canon.