Capitain Imperio Explains: Sexual Selection
The peacock's spectacular tail confounded Darwin. How could something without obvious selective value compete? The answer he came up with, documented again and again, was sexual selection. If one sex prefers some trait, then those with that trait will be preferentially selected for, and over millenia, multiple genes might get involved to produce the elk's antlers, the peacock's tail and so on.
Of course that cannot be the end of the story. Selection of an arbitrary trait would not help fitness. It has to be some trait that is correlated with other less observable traits that do affect fitness. Facial asymmetry in in humans (or animals) is not in itself a direct hindrance to fitness but it tends to indicate that the creature in question does suffer from obvious developmental or nutritional deficits. Unsurprisingly, we overwhelmingly prefer the symmetric.
Men all over the world tend to prefer certain traits in women, and it is not coincidental that those traits are those associated with health and fertility. Similarly, women tend to prefer men with traits that were probably useful to our stone age ancestors - height, evidence of physical strength and athleticism, and verbal dexterity (still pretty useful).
Peahens take a darn good look at the elaborate tails of peacocks, and peacocks go to elaborate lengths to display them. We don't know exactly what the peahens are looking for, but it's clear that they are checking out the details - a study that looks only at size is hopelessly naive - but we can certainly expect that whatever it is, it's correlated with health and fitness.
And scientists are working on it: A peahen's eye view