Mary Sue is a constant issue for writers. She frustrates the reader with her flawless appearance, outrages them with her inability to do any wrong, and bores them with how perfect everybody seems to think she is. It's a trap that most amateur writers fall into, but surely, just removing all those possibly offensive traits would make her a regular character, right?
Mary Sue is not always about how she has radiant purple hair, a perfect seven octave singing voice, and can slice Superman with her katanas with one arm tied around her back. It's about what she does to the story. There's a fine line between a well developed character and Mary Sue, and it's certainly not defined by her appearance, justification (or lack thereof) for her abilities, or how fantastically improbable her backstory is. It's about how the character is defined exclusively by external traits and her actions to the point of shallowness, and about how all other characters are defined by their attitude to her (or him; this trope applies to both sexes). It's about how, in Fan Fiction, she completely overtakes the canon characters in importance. It's about how people act wildly out of character around her and elevate her to a status well above what she should realistically be able to obtain.
In original fiction it's a character who can get away with almost anything, about whom no one can shut up, or a character who is flawed, sure... but seems to live in a topsy-turvy world where flaws function like virtues and are fetishized accordingly. Above all, it is about wish-fulfillment, and wish-fulfillment comes in many forms. There's nothing wrong with a little or even a lot, but when the wish-fulfillment a character embodies starts to warp the narrative and characterization around it, then you may be looking at a Mary Sue, even if she's in disguise.
In the most blatant cases a writer will try to disguise a character's Sue-ness by claiming that she's "not beautiful" before launching into a description of a goddess just without using the word 'beautiful', or by sprinkling her with physical traits such as thinness or a "wide mouth" that have been considered imperfections in the past but are rather more fashionable today. In fantasy or sci-fi examples, an author will sometimes invent a culture where some trait the audience is likely to consider attractive or neutral is regarded as horribly ugly, bad luck, et cetera. The most common of these tend to be a certain eye or hair color, or perhaps something like Pointy Ears indicating partially elven ancestry in a culture prejudiced against elves. But looks aren't the half of it. It is other qualities—abilities, personality (or lack of) and the way that not just the story, but the WORLD revolves around a character, even though it logically wouldn't—that make a character Suetiful All Along. In addition, he or she never wants for attractive admirers.
Note that a lot of this trope is in the tone. For something like historical fiction, even assuming a third person narrator, we would expect that the story is related by someone familiar with cultural mores of the time. So, let's say we're in a time period where fat people are considered the hawtness, and our lead is a thin person who is attractive by modern standards. Averting this trope would mean defining our lead, not in terms of positive exploration (willowy frame, slender legs, delicate arms), but a more negatively tinted one (stick-like frame, spindly legs, stiff arms). It's all a matter of language.
Remember Tropes Are Not Bad: a character who's Suetiful All Along is often more sophisticated than that. Sometimes it's just one eye-rolling event too many that leads you to think back over your hero or heroine's career and wonder "Is she ever wrong about anything that's important?" or "Is there anyone in the story who isn't completely obsessed with him?" Sometimes Sue-ness is occasionally annoying, but livable-with.
Has nothing to do with suet.