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.
Mary-Sue is often abbreviated to 'Sue.' The male equivelant is either Marty-Stu
Your Buffy fanfic has a problem. Her name is Alayne Lorelei Gemma Jeshika Shanna, she has violet eyes and raven hair, curves in all the right places, is more powerful than Willow and a better fighter than Buffy and Faith combined, AND Spike is in love with her. She's a total Mary-Sue, and she's really annoying!"