If you're really interested...
Wikipedia article - Mary Sue
TV Tropes article - Mary Sue
TV Tropes article - Common Mary Sue Traits
TV Tropes article - Mary Sue Tropes
...if I was to sum it up myself...I would say that it could be summed as...the character is never wrong in any major way, and often rarely wrong in any minor way. Any action they take is ultimately for the best, and things that don't turn out for the best is usually because people foolishly didn't listen to them. They are the center of events, often blatantly so, the focal point in regards to everything...in short, people are incapable of solving their problems (at least correctly) without their help, whether that comes in the form of advice or more blatant exercises of power. They are better than the rest of the characters, whether that comes in the form of moral fiber, common sense, intelligence, wisdom, charisma, or simply power levels. All of their enemies are horrible people, and any that can be sympathized with will typically be drawn back to the correct side...ie, that of the Mary Sue.
Admittedly, this is an extreme case, but...that is something of the general gist.
Edit: The easiest way to make sure that character growth doesn't wind up making someone a Mary Sue is to let other people grow along side of them, giving them their own time in the spotlight, giving them important situations that they can solve, and the main character can't...and not making it minor, preferably. Throw in errors of judgment that have real, long-term effects. And, above all, don't try to give the main character some sort of moral or intellectual superiority over every single other character...where the main character is the only person who can see what needs to be done, for example, and everyone else is self-evidently either a fool or blind for not realizing it.