In my mind a Mary Sue/Gary Stu is a character greater than human while being portrayed as a human. They're a deity wearing the mask of a human or animal, should that make them perfect or imperfect. I don't think it's necessarily a bad thing, more a sign of inexperience in characterising than anything else. Given that a lot of MS/GS characters are idealised versions of the creator also corroborates this--as the creator of the character and everything around them, the character themselves can come out on top of every situation because they are projections of the world's creator.
The thing I find interesting about Mary Sues is just how broad the term is and how everyone has a different opinion on what a Mary Sue is. We all have our different interpretations of the trope. I don't know why, but I think that's pretty cool. In my opinion, a Mary Sue doesn't need to be overpowered (Bella Swan needs to be saved constantly and everyone can agree she's a Mary Sue) or a character with unrealistically perfect personality traits (plenty of Mary Sues are terrible people). At its core, a Mary Sue is someone that has the story revolve around them and is the only thing that matters within the story's universe. The supporting cast doesn't matter because the Mary Sue is the only thing the author is interesting in writing about. A Mary Sue isn't made out of character traits, but how the author writes the story around them. The woman in this video explains it really well (also, her other videos about writing are really good, check them out too. If you want, I mean):
A Mary-Sue is someone who unbalances the universe. Take someone like the Mary-Sue I put in my story, Mariella Susella. She unbalances the universe by making everyone fall in love with her at first sight, being more powerful than everyone ever, and overall perfection. In the Pokémon universe, a Mary-Sue could be someone who owns multiple Legendaries, and shinies at that, and wins ever Performance, Contest and Battle easily. This disrupts the balance of everyone having a nonshiny, average team and winning and losing their fair share of battles. The world always revolves around them, OR they’re somehow good at everything with few flaws or weak flaws like “a lot of boys love her and she doesn’t know who to pick”. That’s a Sue trait. Oh, and did I mention Ebony Dark’ness Dementia Raven Way?
To me a Mary Sue is just an underdeveloped OC character. There is potential there for a great character (I think all characters have the potential to be great characters), but the creator doesn't go to the effort to fully develop this character. This gives us a seemingly perfect, no flaws whatsoever, pure, innocent character that just feels unnecessary and boring.
Usually a Mary Sue's flaws are harmless, or have minor consequences, if they have any flaws at all. For example: the most powerful witch in the land can do everything and anything, except for algebra. I find that a lot of authors who think "crap, my character is turning into a Sue/Stu!" just slap a random flaw on their character to make them look developed and call it a day. Unless algebra plays a major role in their high fantasy story about witches, does that flaw even matter? It's also important that flaws have consequences. Maybe the most powerful witch in the land has grown conceited because she knows she's powerful, which results in her losing her closest friends. From this point on, the character has to develop in a meaningful way in order for the flaw to make sense: she has to realize the error of her ways, and either try to make things right, or try to work on her self-absorbtion. If the flaw didn't have consequences, the plot would probably end up more like: the witch is all powerful and conceited, loses her friends, but it didn't matter because a) her friends love her and always come back to her b) she didn't need those friends anyway or c) she doesn't need to change, she's perfect. That would be a Mary Sue.
I’ve been told that I broke the whole ‘Mary Sue’ thing because I made my Oc mess up and have people not like because of it. And apparently my reviewer told me that I broke another common trope.
I generally see a Mary Sue as a person with absolutely no character development. If you already have a 'perfect' character, there is nothing to push the character to be something more. It makes a plot pointless in the grand scheme of things.
I see Mary Sues as characters who physically could not exist in real life. A character who was good at the liberal arts and at the maths and sciences, who got all a's, who plays sports on their highly selective school team, who everyone likes, who also has the time to volunteer at their local center with no gain for themselves? Doesn't happen. But let's switch this up a bit. How about a character who's good at the liberal arts, but can struggle with maths and sciences? A character who gets a lot of a's, but gets a couple b's as well? A character who likes playing sports, but prefers to do it in their local, anyone-admitted teams, because they're not too great at it? A character who has a few close friends that they trust, a few people they detest, and a majority of people that they get along just fine with? A character who volunteers once in a while to get extra credit? I'm only scratching the tip of the iceberg, of course - but now this character is flawed, it's human. Before I changed it, that character could not have existed. That, in my mind, is a Mary Sue.
