A canon character is a fictional character native to South Park. A canon character may also be referred to as a canon or a canonical, though the latter is more properly an adjective.
Canon Characters in Fanfiction Edit
Where there is fanfiction, canon characters are almost always involved. It's rare to find a story set in a canon world that doesn't include at least one or two characters from the original source material. Even in such a story, the canon characters may be related to the original characters in the fanfic, possibly as their ancestors (as in "spawn" fics, wherein all the characters are children of canon characters) or descendents, depending on when the story is set. For the most part, however, people who read and write fanfiction do so because they're interested in the canon characters, and want more stories about them to enjoy.
Good fanfiction strives to keep the canons in character; that is, behaving and speaking as they do in canon. Even if the fic is an exploration of a characterization not displayed in the canon, some reasonable explanation should be given for the changes. For reference, "I felt like it" isn't a reasonable explanation.
Bad fanfiction, on the other hand, often doesn't even try, resulting in canons who are out of character and don't behave like themselves, sometimes to the point that they literally aren't themselves anymore.