A story or situation in which the main consideration is one of suspense.
'Cliff-hanger' entered the language as a description of the various short melodramatic serial films which Hollywood produced from 1914 onward. The best-known of these are 'The Perils of Pauline' and 'The Exploits of Elaine', starring Pearl White and 'The Hazards of Helen', starring Helen Holmes and later Helen Gibson. The films' plots were as predictable as their titles and the public perception of them is of a heroine being left facing certain death at the end of one film in a series - tied to railway tracks, hanging from a cliff by her fingernails etc. - only to be saved at the beginning of the next. In fact, this isn't quite correct. The films in the series didn't run as one long sequence but each had an independent storyline, which usually began with the heroine being found in a situation apparently facing certain death, only to escape and thwart the bad guys by the end. The Perils of Pauline is the name now best-remembered, although the other two films mentioned above were more successful at the time.
It seems that the term 'cliff-hanger' wasn't coined until well after the heyday of what we now think of as 'cliff-hanger' films. The first mention of it that I have found in print is from the Illinois newspaper The Edwardsville Intelligencer, March 1936:
Maybe you remember Helen Holmes, of Keystone, Kalem, and otheronce-famous companies? "The Hazards of Helen" was her greatest cliff-hanger serial.