A fan fic that is particularly dark in atmosphere and has disturbing concepts. Is usually full of angst, torment, depression, violence, rage, abuse, insanity, sorrow, horror... Lots of negativity.
Dark fics are based off of series that have a brighter, happier mood, or just have too much humor in it.
It wouldn't really make sense to base a dark fic off of a dark series.
I read a really dark fic of Naruto where Naruto keeps getting tortured and Sakura is always getting raped.