What is a Mary Sue?
Mary Sue is a term used to describe the 'perfect character.' The less common male alternative is 'Gary Stu'.
Mary Sues are those characters that are 'super popular', pretty, unique, and have no character flaws. This makes them uninteresting and rather boring to interact with, as they can solve any problem in under five minutes because they have a huge, long list of powers and abilities, and can't do wrong.
Why are they received negatively?
While powerful characters are interesting and can be very fun when done correctly, when done INCORRECTLY they become quite annoying . In roleplaying, they're difficult to interact with, and in writing they can be very boring to read.
As characters, they tend not to have many or any bad traits or flaws, making them hard to relate to and unbelievable, and they tend to try people's patience when forced to interact with them.
There is hope!
How to avoid making a Mary Sue
Give your character some flaws! Even primarily good characters have negative traits. When making a protagonist, many people can accidentally make them Mary Sues in an effort to make them good, kind, and brave, but even the nicest person has some character flaws.
Push extremes when thinking of flaws!
If they have firm beliefs about right and wrong, make them stubborn or hot-headed. If they're a jokester or funny, make them annoyingly talkative, overly honest, or have them go too far with pranks.
HOWEVER, people can take this advice the wrong way. Making a character 'too caring,' can work, but only if they're caring for others to the point of foolishness or too trusting, getting them in trouble time and time again.
If your flaw is 'overly caring', make sure it is a flaw and not another good trait disguised as a bad one.
Dealing with other people's Mary Sues
When roleplaying, collaborating, or working with other people's OCs, you may encounter someone else having a Mary Sue character. If it gets too out of hand, refer them to this page and/or the others mentioned above.
However, if they're aware they're behaving annoyingly and not willing to put in effort to make their character better, they may just be trolling you. Try your best to humor them or ignore them, whichever works best, and best of luck to you.