I've always found this absolutely hilarious. There are plenty of slight variations on the test, however the one I linked is pretty comprehensive.
A Mary-Sue is basically a character created who fulfills the secret wishes and desires of its writer, in such a way that the character is unbelievably flawless and filled with clichés. Or, if the character has flaws, they are often shared with their inventor and are miraculously overcome in the course of the story.
I think I find it so funny because each question identifies so strongly with the 123504196 teenage fiction books I read when I was about 9, about kids who move to a new school, make no friends but then get transported to this fabulous world where they make a lot of friends and save a lot of people, or something along those lines.
Someone's version (courtesy of Google Images) of an Anti Mary-Sue. Yes, she is spectacularly normal, for a witch, but I don't think you can actually have magical powers without being levitated to slight Mary-Sue status. I can't imagine a single person who doesn't want to be magic, so there's got to be some wish fulfillment involved here, no?