Twincest is a type of incest fic that has the relationship be between twin characters in any particular canon. Twincest is most often slash between male twins, but lesbian and het twincest also occurs.
Twincest fics often turn out poorly due to the amount of squick they naturally contain, but if done well, they can be extremely good. The visceral unease raised by a taboo relationship can be deliberately used to make the readers wary of the characters (for a canon example, see Jaime and Cercei Lannister). On the other hand, the combination of deep transgression with deep love striving to overcome it can make for a tense and enjoyable romance, even if the authors and the readers who like it would never condone incest in Real Life. The trope is popular enough that it's successfully played up by the well-known parody manga/anime Ouran High School Host Club: twins Hikaru and Kaoru Hitachiin use a "forbidden brotherly love" act to cater to the club's clients.
The PPC does not condone twincest or any other type of incest in Real Life. It also takes particular exception to poorly written twincest that ignores canon characterization, human psychology, and/or deeply ingrained social norms in favor of cheap thrills.
Fred and George Weasley from Harry Potter, Dipper and Mabel Pines from Gravity Falls, and Elladan and Elrohir from The Lord of the Rings are often victims of bad twincest.