Often, especially deluded, obsessive, or unimaginitive writers of fan fiction write themselves into their stories, in a role that usually fulfills their fantasies. "Mary Sue" is the generic term for this character, and the story itself, as in "Wow, buffygirl_23 really cranked out a first-rate Mary Sue this time!". Usually, Mary Sue is attractive, smart, witty, and anything else the author wishes he/she was. Mary Sue frequently saves everybody, and earns the respect (and often the hot, sweaty monkey-love) of the actual characters from whatever movie or TV series the story is about.
I support everybody's right to produce fan fiction of whatever quality they desire and are capable of producing. The really funny thing about Mary Sues though, is that many have been published as "official" series novels! Many a Star Trek novel features a minor character who is the same gender as the author and seems to get an inordinate amount of attention paid to them. :^)