A cliffhangeris a plot device in which the final moments (the denouement) of any story are truncated, leaving the reader or viewer without plot resolution and, usually, opening up new plot points. The cliffhanger is found most commonly in serial writing forms: the monthly comic book, the weekly TV show, the movie trilogy, and book series.
A cliffhanger is designed to propel the action forward. By leaving the reader or viewer with an unanswered plot motif, it encourages people to come back to find out the answer. The standard issue for TV shows and comic books is usually to end with the phrase "To Be Continued", as opposed to the also traditional "The End". A surprise kiss (think Ross and Rachel's first kiss in Friends), shocking deaths (pretty much any comic book death - Captain America, Superman, or Batman among them), or other pivotal plot moments are often saved for the cliffhanger, where they can have a lot of impact.
While the term cliffhanger is relatively new (coined sometime in the early twentieth century), its use as a plot device can be found in the novels of Charles Dickens. Dickens' novels were serial novels, a popular publishing type in Victorian times, meaning that they were published chapter-by-chapter, in magazines, over the course of several months or years. This is why, even when reprinted in traditional book format, each chapter's ending still ends with a new mystery or twist.
The cliffhanger is related to but is different from the twist ending, a common movie trick, sometimes employed in books as well. In the twist ending, a revelation at the denouement changes the entire outcome of the plot or the meaning of the story, much in the same way the last lines of a poem can change the entire poem's theme.
A good example of a twist ending is Some Like It Hot (pictured), wherein a male character, Jerry, pretending to be a woman to escape the mob and having convinced another, seemingly straight, male character, Osgood, to fall in love with him, reveals to Osgood that he's in fact a man. Osgood then responds with, "Well, nobody's perfect." The film ends, and the audience is left to wonder if Osgood knew all along. In other words, the twist ending is still a finished ending, while a cliffhanger is meant to go on.