What is Mary Sue?
1.
See
Victim!Sues: The Victim!Sue is your whiny, wimpy, pathetic female character who can't seem to do much of anything except cry and get herself into trouble that the romantic interest of the fic has to rescue her from.
Warrior!Sues: The Warrior!Sue is usually loud, obnoxious and (of course) an amazing warrior. She'll usually have some tragic past that led her to become a warrior, and she'll upstage all of the
Mage!Sue: Similar to the Warrior!Sue, the Mage!Sue has amazing stregnth in magic, or has a magical power that nobody else has. She'll usually wind up upstaging all of the magical characters of the series.
Punk!Sue: Also called Noncomformist!Sue or Goth!Sue, the Punk!Sue is usually written by female beginners in the 11-15 age group. The Punk!Sue is loud, obnoxious, annoying and generally the type of person who you'd want to send off to boot camp for six months. The Punk!Sue almost always has angst coming out of her ears and isn't really a bad person, she's just oh!-so-angry at whatever tragic past the author has chosen to give her. The Punk!Sue is based on what the 11-15 year old author thinks is "cool" and wishes she could be. This includes Evil!Sues.
Misfit!Sue: This includes all Sues who are supposedly geeks, nerds, misfits, etc. Usually, the Misfit!Sue doesn't start out as inhumanly beautiful, but winds up getting a makeover and finding out she had the potential to be a guy-magnet (or girl-magnet, depending on the genre) all along. Also includes the "My parents want me to do this but I want to do that and it's not fair!!one!" type of Sue. Usually, this Sue is very bookish and smart, but will find some sort of physical talent nobody expected and become a star as a result.
Another thing to note is that a Sue will usually have a completely off-the-wall name, like "Viquetoria". The more wierd and pretentious the name of the character, the more likely it is that she's a Sue.
Finally, Sues often have wierd, improbable or impossible bloodlines. A secret half-elf child of Elrond and a nameless human would be an example of this. A character who was Dumbledore's grandchild and Tom Riddle's daughter would be another example.
The character in the HP fanfic was a complete and utter Sue. She moved across the street from Harry. She was beautiful, smart and pretty. They fell in wuv almost immediately. She threw all of the characters out of character and generally upstaged everyone. It was quite obnoxious.
2.
The most common type of Mary Sue is a character based an the author's idealization of themself. Furthermore, because the author is imagining a preferred version of themself, and because faults are overlooked in favor of optimization, a Mary Sue tends to have only superficial resemblance to the author, sharing similar likes/dislikes and a similar spirituality (when applicable), but objectifying things such as worldview and relationships. This type of Mary Sue is more common simply because it's easier to write and is more appealing to the author. This Mary Sue is found in fanfics and original fiction alike. Yes, Mary Sues abound even in professional writing.
The other type of Mary Sue is a character intended to be an ideal match for another, appearing almost exclusively in fanfics. In this case, "ideal match" means that the character's positive traits are exaggerated to render impossible any competition for the love interest. Arguably more pernicious than the "self-idealization" type, the "ideal match" type by its very nature prevents compelling character or plot development, which the "self-ideal" Mary Sue may be able to avoid.
Self-idealization: "That fic was ridiculous. I could overlook the atrocious grammar, but not such an obvious and annoying Mary Sue. What's the point of releasing a story to the unsuspecting public if it's only written for the masturbation of the author's ego?"
Ideal match: "It's hard to find any other story that's so dull as one that has an ideal match Mary Sue in it. What is there to be interested in if the pair never has any trials to overcome?"
See