Mary Sue-ism is when your main character, or any other character, is portrayed as "perfect" or that, against all odds, everyone is completely in love with that character. No matter how horribly flawed, idiotic, unintelligent, clumsy, unaware, oblivious, and downright ridiculous that character may seem. *coughBellacough*
(You know what, I think I might have to have a post that is dedicated to all the things wrong with Bella that Meyer did not intend. I really should.)
The short and sweet definition from Wikipedia goes as following...
I know when you hear the words "Mary Sue" you immediately think of the main love interest of our very own Spiderman, right? Or at least that's what I think of. The term "Mary Sue" actually originated not from the popular Spiderman comics and movies, but of a Star Trek fan-fic.
The Urban Dictionary describes a Mary Sue as the following....
I love the urban dictionary sometimes, I really do. Especially times like now when I can't think of a better way to put it.
A female character who is so perfect that she is annoying. The name originated in a very short Star Trek story that mocked the sort of female characters who showed up in fanfiction. It usually refers to original female characters put into fanfiction, but can refer to any character.
Mary-Sues are characters who are usually extraordinarily gorgeous, amazingly talented, unusually powerful, and exceedingly attractive to whoever the author has a crush on. They often possess ridiculously fancy and pretentious first names -- Angel, Raven, Jewel, Lorelei Bianca Julia Marizza Snape -- and are very, very annoying.
The obvious example is Bella from Stephenie Meyer's Twilight series. Just another reason I would not recommend that book to anyone. No matter what this girl does, everyone loves her. She has guys drooling (sometimes quite literally) after her every step. No one gets mad at her. She's literally "perfect"!
Before I go off on that soapbox, let's rein in the topic. Bella's only flaw *ahem* make that the only flaw given to her on purpose would be clumsiness. I know we did a big circle here, but my point is that Bella Swan is a Mary Sue. Points against her: everyone loves her, she's some sort of freak of nature (in more ways than one, of course, but I mean with the vampire-y powers), everyone loves her, she gets good grades, makes friends easy (?), and even smells good!?
Mary Sues sever any really connections that could offer between themselves and the readers. The only thing they can give is an idea of "perfection" that the readers will never achieve, and that bond is fragile. It's like having friends just to get a hold of their money. First off, it's not nice. Secondly, it's not real friendship and it won't last.
The point is don't write these "perfect" people into your story. They drag the story down. Here's a great resource on Mary Sue's http://www.fictionpress.com/s/1440163/1/The_Official_Mary_Sue_Manual. It is mainly related to Mary Sues in fan-fiction, but it can relate to novel writing too. There's some great advice there on how to avoid writing them.
Hope I cleared some things up. Have a nice spring and keep writing!