From Bulbapedia, the community-driven Pokémon encyclopedia.
Fanon is a term used to described influential or widely believed fan theories about the fictional elements of a series. The term is a portmanteau of fan and canon (which is used to describe known facts about that series). Those fan theories are often speculation based on stated canon facts, but sometime only bear a tenuous relation to the facts as stated, and it is possible for fanon to circumvent or contradict established canon. Fanon is distinct from headcanon, which describes the multiple fan theories a single fan believes in, whereas fanon describes a single fan theory that a large number of fans believe or used to believe.
In the Pokémon franchise, while fanon about the Pokémon anime is the most common type, there are also widely known fan theories about the video games, and about less common aspects of the franchise.
Nature of fanon
Most fanon begin its existence as the personal theories (headcanon) of one or a few fans. As they share their theories with other fans (both in discussion or via including it in their own fanworks), other fans begin to adopt the theory in turn, or to use it as the basis for their own theory. These fans in turn help spread the theory to more fans, leading to the theory becoming widespread and influential, and thus fanon. Even if belief in the theory later wanes, it remains fanon.
In most cases, these theories complement known canon facts. For example, in the original games, it is canon that the rival has a Raticate when encountered on the S.S. Anne. It is also canon that the protagonist next encounter him at Pokémon Tower in Lavender Town, a Pokémon cemetery, where he does not have the Raticate any more. This has led fans to speculate that that Blue's Raticate died at some point between the two encounters, possibly as a result of the battle with the protagonist on the S.S. Anne, a theory that has become fanon.
In other cases, fanon theories can seek to circumvent or outright ignore established canon. For example, a fanon theory proposes that the Pokédex entries found in the game and anime actually describes myths and folktales about various Pokémon species, rather than accurately portraying the abilities of those species. In that way, fans who find the abilities described in the Pokédex entries to be unbelievable or exaggerated are able to dismiss the more egregious claims as legends rather than facts.
The term "fanon" applies only to beliefs that are not stated to be correct in the source material. If a fanon theory is later confirmed by the series, it then becomes part of canon, and is no longer considered fanon. It is also limited to belief about the fictional elements of the series (such as plot, characters and setting). Speculation about real-world elements, such as the speculation surrounding possible third generation remakes, prior to the announcement of Omega Ruby and Alpha Sapphire, was not fanon. Likewise, speculation concerning why certain episodes of the anime were banned is not fanon.
Multiple series and fanon
The Pokémon franchise includes multiple distinct series, each with their own canon, or continuity, such as the anime, main series games, Pokémon Adventures manga, etc. Each series has its own set of canon facts, which are distinct from one another. These facts do not necessarily hold true for other series of the franchise. For example, while in the Anime, trainers are said to begin their journey at ten, this is never stated to be the case in the main series video games, and the protagonists whose ages are known are older than ten.
When it becomes popular fan belief that a canon fact from one of the series holds true in another Pokémon series, that belief is also a form of fanon.
Shipping, the belief that two characters are or should be romantically interested in each other, is one of the best known examples of fanon. However, not all named shippings represent fanon theories. While some, such as RocketShipping are extremely influential theories, others, such as those involving characters who have never met on screen, are neither popular nor influential (and thus, not fanon). In addition, a number of named shippings are humoristic in nature, and not actual theories supported by fans. These, likewise, are not part of fanon.
Likewise, confirmed shippings, such as BalanceShipping (Norman and Caroline, who are known to be a couple) are canon, and thus not fanon.