Literally, the vagina, although in the United States, the slang definition of this word is infinitely more weighted than its literal implication. It is commonly regarded as the foulest derogatory word ever invented. If it is ever used, it is only ever used in reference to a woman, and is meant to suggest that she is supernaturally bitchy, nasty, and/or mean-spirited. People who use the word in any other form than its literal meaning during dirty-talk infused sexual intercourse are looked down upon as sub-human filth.
In the British Aisles, however, the word is quite commonplace in culture, and is thrown around by working-class folks. It can be used to refer to either a man or a woman, they might be mean-spirited, but they may also be dim-witted, arrogant, cowardly, boorish or just someone who makes one's life miserable. In the film "Sexy Beast," Ben Kingsley and Ray Winstone use the word "cunt" approximately sixty-five thousand times each.
Englishman: "I was dining at a Denny's establishment a fortnight ago, and the conversation eventually turned to politics. I made the remark, that the problem with Tony Blair is he's a cunt... and by jove, the whole restaurant went so quiet you could have heard a bloody pin drop!"
American: "You said the c-word out in public? Oh my gosh... I think I need to sit down."