This sentence has come to be the stereotypical starting line for fictional novels and tall tales everywhere, most particularly bad novels. It is used to indicate that a story is commencing, although it is rarely followed by an actual story. Generally, it indicates a hackneyed story of the adventure type, although the details of the story are less important than the fact that the story starts with one of the best-known starting lines in English literature, indicating that it will likely not be a serious literary endeavor intended to stand on its own right.
However, the original appearance of the line was not in a great and famous work, but rather in a mostly-forgotten novel by a mostly-forgotten novelist. The line was in fact grabbed from the jaws of obscurity by the mostly-unknown Professor Scott Rice, who used it as the inspiration for a slightly famous contest to find the Worst Starting Line Ever. The Bulwer-Lytton Fiction Contest is worth checking out if you have not yet discovered it, and is the source for the spread of "It was a dark and stormy night" through our popular culture.
The original line, and yes, it is all one sentence, in its complete and original form:
"It was a dark and stormy night; the rain fell in torrents -- except at occasional intervals, when it was checked by a violent gust of wind which swept up the streets (for it is in London that our scene lies), rattling along the housetops, and fiercely agitating the scanty flame of the lamps that struggled against the darkness."
--Paul Clifford, by Edward George Bulwer-Lytton (1830)
It is somewhat inexplicable that this lipid lump of prose has become so overwhelmingly recognizable -- but quite understandable that no one recognizes where it came from. Part of the blame for its fame must fall on Snoopy from the comic strip Peanuts, as he used this line in nearly every book he wrote.