The notion that a woman should be, or that a man wants a woman to be, unavailable to everyone but her boyfriend/husband/sugar daddy/etc. More and more, the saying is becoming irrelevant, just an artifact of feminism and a handy allegory for little girls showing a tendency to be more dependent than is healthy. It's something college girls can get safely worked up about, knowing that the stereotype can't be forced on them.
There was a time, however, when a man could have specified these qualifications for his consort with a straight face. Even now, there are still men (and women) who feel that this describes the ideal woman.
This sort of thing is pretty common in patriarchal societies, where the male is the head of the household and sole provider for his partner and offspring. Most have an unspoken tradition that it's the wife's duty to put out for her husband and only her husband. And she has to like it. As more women work and fewer are beholden to their spouse or boyfriend for food, shelter, and Prada, the idea of "A virgin in the parlor" seems increasingly contrived.
The corollary to this idea is the virgin/whore complex, which is more descriptive of a single woman's predicament. A wife is expected to express her sexuality in one specific situation and only that one, but then as exuberantly as possible. A single girl, on the other hand, is damned if she does, damned if she doesn't. If she doesn't give it up, she'll be no good in the bedroom, and if she does, how can she show her face in the parlor? A traditional girl's only real option is to get married the day she hits puberty and duck the question altogether. (I'm not joking. That's pretty much how they did it in medieval societies.)
"A virgin in the parlor" is becoming more a lifestyle choice, less a definition of what a woman must be. Some couples still operate this way, and in others, the man takes his turn getting tied up every once in a while, too. For a long time, in a number of societies, it wasn't optional. Even as it becomes a less prevalent mindset, it's still a defining part of the identity of women and the history of feminism.