It isn't entirely clear what is driving the increased anxiety many women are now experiencing about their vulva. One theory is that pornography is driving this trend, and that there is some sort of ideal vulva represented in porn. But as Stoya, a prominent porn star, has noted, pornography, in general, may not unequivocally be the culprit (post here - not that she's claiming that pornography doesn't have an effect on preferences). She also notes that men don't really seem to care about the size of their partners' labia.
Another theory suggests that the increase in labiaplasties is the result of marketing by plastic surgeons. So, for example, a woman visits a plastic surgeon's website for some other procedure, and sees marketing for labiaplasty, which presumably indicates that larger or asymmetrical labia are problematic. This is potentially internalized, leading to a desire to seek out labiaplasty.
Assuming pornography is responsible, however, it isn't clear if women are feeling down on their vulva because they're watching pornography and comparing themselves (specifically to those actresses with small inner labia - most actresses have average or larger labia), or if men's consumption of pornography is affecting male preferences, leading to demands about their partners' vulva (perhaps the more likely explanation?). If average and smaller labia are supposedly more desirable, then why are there very popular web sites out there dedicated to the worship of large labia (e.g., here - very NSFW)? It's also possible that the vulva is simply another part of the body that can cause anxiety, and that the more media exposure vulva dissatisfaction gets, the more anxiety that is created.
There's very little good data addressing this issue. Here is one of the few studies:
Miklos, J. R., & Moore R. D. (2008). Labiaplasty of the labia minora: Patients’ indications for pursuing surgery. Journal of Sexual Medicine, 5, 1492–5.
They found that 37% of women who underwent labiaplasty did so only for cosmetic reasons. Another 31% went through the procedure for both functional and cosmetic reasons. The other 32% had labiaplasty only for functional reasons. Overall, 6.9% stated that they were influenced by their partners (in 2 of 9 cases, by female partners!).
The paper can be found here.
Anyway, another project about labiaplasty and women's relationships with their vulva, despite the misleading name (vagina?):