I'll try my best not to cut and paste the entry from Wikipedia here, but in my own words, this is a spirit of a woman who lived during the time of the Samurai in Japan. She was a rather adulterous and vain woman in life. When her husband came home (from presumably war) and more importantly, when he discovered his wife's infidelity, he slashed her face from ear to ear. She was given a 'Chelsea Grin', and she spends long foggy nights or just in general looking for victims wearing a surgical mask or other form of veil.
This spirit will ask all who she encounters if she is beautiful, and once she removes her veil, showing her horrid scars, she'll ask again. If the individual is a male, she'll probably just straight up kill you which makes sense because a man cut her face up to begin with. However, both genders have a chance at getting away from her- if they can tell her (presumably with a straight face), that she is "So-so" or "Just alright/O.K." the spirit will become distracted, and then the victim can make their escape.
A point of mention is that the answer that one can give this spirit to confuse it long enough to make one's getaway is constantly changing. Kuchisake-onna is getting smarter and smarter it seems.
What's chilling is that apparently have been public panics in Japan about this spirit hunting down children, whose oh so innocent answers and even screams proves to be their doom. First in 1979, and apparently a coroner in 2007 found hard evidence to support the idea that a woman who was similarly afflicted was chasing children.
Another similar entity was rumoured to exist was said to haunt South Korea, wearing a red mask.
Anyways, here's the Wikipedia article if you want to read the whole thing.
http://en.wikipedia.org/wiki/Kuchisake-onna
