Well, it's more who the author would
like to be. As
this website puts it:
Mary Sue is any original or deeply altered character who represents a slice of his/her creator's own ego; s/he is treasured by his/her creator but only rarely by anyone else. More negatively, a Mary Sue is a primadonna (usually but not always badly-written) who saps life and realism out of every other character around, taking over the plot and bending canon to serve his/her selfish purposes.
From
Dr Merlin\'s Guide to FanFiction: You already know Mary Sue. Mary Sue is the perky, bright, helpful sixteen-year-old ensign who beams about the ship. Everyone on the ship likes Mary Sue, because Mary Sue is good at everything. Mary Sue is an engineer, a doctor in training, a good leader, an excellent cook, and is usually a beautiful singer. Mary Sue often has mental powers that may manifest themselves as telepathy, precognition, or magic. Her past is tragic, more so than any other character on the series. (Many Mary Sues have a backstory that reads like a V.C. Andrews novel. This is a clue.) If Mary Sue is very young, she is often the offspring of one or two already established characters. If she's a little older, she will probably end up sleeping with the author's favorite character. Sometimes, she fills both roles. Her name is often the author's name, be it a net.name, a favored nickname, or the author's middle name (this is seen in the most famous Mary Sue of all time, Wesley Crusher, who was named after Trek creator Eugene Wesley Roddenbery). By the end of the story, Mary Sue will be in bed with the desired character, will have beamed away amid cheers from all the regulars, or will be dead, usually accompanied by heavy mourning from the cast. The reader, on the other hand, will be celebrating.
And this site also hosts the
Mary Sue Litmus Test .
Mary Sue and how to avoid her .
And finally, for a bit of fun, how about the
Mary Sue Generator? 
Wendy
