Imagine you're a female cardinal and you're looking for a mate. Before you are three males. Which one should you choose?
Normally, female cardinals look at their prospective mate's ornamentation, like the size of his black face mask and the color of his breast plumage and of his bill.
Studies have shown the ornaments on both male and female cardinals communicate information about the bird. In fact, each ornament sends a different message, so that by assessing several of them, you can get a sense of the bird's overall condition.
Now, ornamentation means different things for males and females. For example, if you're a female, a large face mask indicates that you're good at defending your nest. But if you're a male, it indicates a lower rate of reproductive success.
It's possible that there are different pressures on males and females in terms of behavior. For example, with a female cardinal, you might want to know when in the season she first nests, and how she cares for the young, qualities that are correlated with larger body size, brighter bills, and redder underwing feathers.
With the male, large body size and good physical condition, qualities which help him defend territory, correlate with the color of his bill and upper breast.