Consider the following hypothetical scenario. The process of choice is not entirely straightfoward, however.
Females are unable to assess directly the quality of the males.
Instead, males advertise their quality via a display of some sort, for example, with bright plumage and a long flamboyant tail. This advertisement is a handicap in the sense that it is energetically costly and possibly dangerously conspicuous as well. As a male adopts brighter colors and a longer tail, his chance of surviving declines. But the cost of producing a long tail varies among males. A weak and sickly male can scarely afford to put energetic resources into production of mere ornaments, and moreover he would have a hard time escaping from a predator if his flight was hindered by a long tail.