Female animals must often choose their mate based on
immediate impressions alone, as dictated by
predatory pressure and short
life span. Female
green tree frogs look for the males that call loudest and most often, female
guppies choose the most brightly colored males, and female
mallards the males who display the
courtship ritual most often. On casual observation this kind of choice would seem contrary to
natural selection, which says that the males most
fit for survival should get the most chances to mate. That is, it seems as though males should be selected by
evolution to be best at finding food and evading predators, rather than wasting valuable resources on showy display.
In 1975, a husband and wife team of Israeli researchers, Amotz Zahavi and Avishag Kadman-Zahavi, wrote a book named The Handicap Principle: A Missing Piece of Darwin's Puzzle to explain why. Their theory, in a nutshell, is that only the males which are most fit to survive can afford to expend resources on otherwise-worthless courtship displays. A male peacock can grow a beautiful array of tail-feathers because he is adept at escaping enemies and maintaining good nutrition; and male green tree frogs can afford to spend time sitting still and loudly making himself a predatory target because he is already well adapted. This viewpoint also makes sense because it makes sure that the males' signalling unable to be "faked" by an evolutionary shortcut, so the females get an "honest" signal to use in their choice.
Depending on environmental conditions, sometimes this signalling can get out of hand, resulting in a state of runaway selection. In the model proposed by researcher R. A. Fisher this begins as selection based on their plumage, which integrated with the handicap principle, means a choice based on survival fitness. Thus, there is have natural selection in action. Because of females choosing based on male plumage alone, females are also selected for better discernment of plumage; so there will be selective force pushing towards even more plumage and even better discernment, and so forth. This will eventually bog down actual natural selection based on fitness, and the highly-selected/well-plumed members of the pool will die back strongly, keeping everything in balance.
In a somewhat muddled metaphor which you might be better off ignoring, I conceptualize this entire process as being akin to dominance and recessiveness in genetics. Dominant traits (like well-plumed males) will tend to be visible more often, and will usually be more important to survival. However, recessive traits (like poorly-plumed males and the females who can't tell the difference) will continue to exist in some measure, and become vitally important for species survival every now and again.