An obsessive and dangerous female, in pursuit of a lover who has spurned her.
The expression 'bunny boiler' derives from the 1987 film Fatal Attraction, written by James Dearden and Nicholas Meyer. The plot centres around Alex Forrest (Glenn Close) obsessively pursuing her ex-lover Dan Gallagher (Michael Douglas). The phrase comes from the plot device whereby Forrest, in a fit of frenzied jealousy, boils her erstwhile lover's daughter's pet rabbit. Gallagher's suspicions should have become aroused earlier, when Forrest was trying to persuade him to meet her, when she said "Bring the dog, I love animals... I'm a great cook."
At the time that the phrase first came into general use it referred to someone unable to remain rational at the end of a romantic relationship. Very quickly that usage became moderated and it came to be used, often with some degree of irony, in much less extreme situations. Any needy, possessive or even just mildly annoying woman is now liable to be described as a 'bunny boiler'.
The phrase is the modern equivalent of the woman referred to in the expression 'Hell has no fury like a woman scorned' which, in the competition for 'best-known phrases attributed to Shakespeare that were actually by someone else', runs 'music has charms to soothe the savage breast' into a close second place. Both these phrases were coined by William Congreve in 1697, in the play The Mourning Bride. For reasons that I'll leave others to explain, it is only women who are thought to become unhinged by being what is now graphically known as 'being dumped'. There's no male equivalent of 'a women scorned' or a 'bunny boiler'.
As 'bunny boiler' is a recent phrase with such a clear source we are able to trace how it has found its way into popular use. It wasn't directly from the film, as the epithet isn't used in the dialogue, nor any of the advertising blurb used to promote it. As to who coined it, that's not clear, although it may well have been Glenn Close. The first use of it in print is from an interview Close gave to the US magazine the Ladies' Home Journal, reported in the Dallas Morning News on 6th December 1990:
"There's nothing like portraying a psychopathic bunny-boiler to boost one's self-esteem, Glenn Close tells Ladies' Home Journal."
Popular phrases that have found their way into the language since the emergence of the Internet appear first in online discussion groups, blogs and online newspapers. The earliest large archive of online colloquial messages is that of USENET groups, but Bunny boiler isn't found there until 1994, nor does it appear more than once or twice in the archives of US or British newspapers before that date.
The section of the public that has most enthusiastically adopted the term into its language is street-wise young adults - not a group that would normally be expected to read the Ladies' Home Journal. The phrase is now a commonplace on TV reality shows and soap operas; for example, in an August 2004 piece by Danielle Lawler and Emma Cox about the UK TV show Big Brother, headed Big Brother: Bunny Boiler we find:
And the love-struck Geordie has already warned her boyfriend Stuart Wilson's army of female fans to stay away. She hissed: "I can be an extremely jealous girlfriend ... and Stu won't even be looking at another girl when he comes out. I can see how people think I'm a bunny boiler."
If the phrase were a commercial product then marketing people would say that it reached its target audience in 1994. It certainly saw a sudden and widespread use from then onwards and is now a commonly used phrase. Fatal Attraction was released in 1987 and Close referred to the phrase in 1990. Newly coined terms appear to spread in the community like viruses and, like flu viruses, they float around in the populace until they reach a threshold of infected cases, above which they spread rapidly. It appears that 'bunny boiler' got to that point sometime in 1994.
See other phrases that were coined in the USA.