A canon character is a fictional character native to a particular book, television show, movie, comic book, video game, or other canon universe. A canon character may also be referred to as a canon or a canonical, though the latter is more properly an adjective.
Usage Note: in some circles, such as the Neopets role-play forums, canon characters may be referred to as original characters, since they are the original inhabitants of the 'verse. In the PPC, however, original characters are original creations of the fanfic author rather than the canon author.
Canon Characters in Fanfiction
Most people who read and write fanfiction do so because they're interested in the canon characters, and want more stories about them to enjoy. Therefore, 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 a fanfic that focuses on original characters, though, the OCs may be related to the canon characters, possibly as their descendants (as in "spawn" fics, wherein all the characters are children of canon characters) or their ancestors, depending on when the story is set.
Good fanfiction strives to keep the canons in character; that is, behaving and speaking in ways that feel consistent with their behavior and speech patterns in canon. Even if the fic is an exploration of a characterization not displayed in the canon, good fic provides a reasonable explanation for its divergence from canon and a logical progression from the canon point A to the non-canon point B. For example, a good Evil!Harry fic could have Harry befriending Draco Malfoy rather than Ron Weasley as its point of divergence. From there, the fic could show how that relationship and the others he forms because of it influence Harry to despise all Muggles like the Dursleys, who treated him so poorly, and to value status more than goodness. The fic would also have to address the parts of Harry's life that wouldn't change just because of his friendship with Draco, such as the fact that Snape would still hate him and his other teachers would still try to exert a positive influence on him, but that's one way a story could begin to set Harry up to be more sympathetic to Voldemort's cause.
Bad fanfiction, on the other hand, often doesn't even try, resulting in canons who are out of character and act in ways that are inconsistent with their canon portrayal, basic psychology, or both. Sometimes to the point that they literally aren't themselves anymore. While multiple valid interpretations of a single character can exist, a valid interpretation relies on the support of evidence within the canon. The more an alternative characterization has to ignore parts of the canon or invent scenarios not present in canon to make sense, the less valid it becomes.
Common explanations for writing characters OOC that are neither reasonable, logical, nor valid include "I felt like it," "I was sugar high," and "because of love." (The latter usually involves a Mary Sue or a case of bad slash.) These are properly regarded as stupid.
Humor and Parody
Deliberately writing a character OOC for the sake of humor is sort of an exception, but sort of not. Successful humor is based on truth, or at least what is widely perceived to be the truth. Therefore, in order to be funny, a good parody must take the true nature of the character into consideration just as much as a regular fic. Exaggerating a character's existing traits (positive or negative) is funny only when we recognize something we love or hate about the real character within the parody. Tacking on random, absurd traits that the character never had is doomed to be seen as dumb.
Canon Characters and the PPC
People generally choose to become PPC agents because of their love and respect for canon and canon characters. All agents have characters who are their particular favorites, and many have designated Lust Objects. Agents tend to get very angry when their favorites are messed with by badfic. This is bad for the Mary Sue or wraith behind the fic.
The PPC has a non-interference policy regarding canon characters, which means that agents are discouraged from interacting with them during missions. This is partly to prevent embarrassing incidents of squeeing, glomping, and general fangirling/fanboying. Agents are especially discouraged from interacting with their Lust Objects. They have partners to keep them under control if necessary, and may be prescribed No-Drool videos if that is not enough.
The policy is also in place because the existence of the PPC must be kept secret, since the knowledge of it is non-canon to just about every plot continuum. The agents are aided in this by their disguises, which help them blend in with the background, and the Somebody Else's Problem field generated by their flash patches. They are also equipped with neuralyzers to erase the characters' memories of the badfic and the agents at the conclusion of a mission.
That said, it isn't unheard of for agents to seek help from canons (and then neuralyze them afterward), and there are a few canon characters who know of the PPC. These characters may be omniscient, like Aslan or Eru; or otherwise impossible to neuralyze, like Death or the Bronze Dragonflight; or they might simply have a talent for knowing things they shouldn't, like Gaspode. These characters and others with OOC resistance or immunity tend to make useful allies, since they may perceive the wrongness inflicted on the people and places around them by badfic and want to help the agents fix it.
Replacements, expys, and look-alikes of canon characters may be recruited if they're reasonably distinct and good characters in their own right. If they can't be recruited or neuralyzed and left to make a new life for themselves, they may need to be assassinated.