In nature, it is common for animals to be sexually dimorphic; in other words, males and females look different. There are some extreme examples of sexual dimorphism. You may be familiar with peacocks, where the males are elaborately ornamented and colourful.
There are some trends; for example, in general males tend to be the brightly ornamented ones while females are cryptic, or dull-coloured. Females are often larger because they need to carry the young or eggs.
Perhaps you are not familiar with the peacock spider, which is a Salticid or jumping spider. Among the jumping spiders, the males are often smaller and more brightly coloured, and they dance to attract the attention of females.
If you’re not familiar, I highly recommend this video:
This same trend is often found in birds. The males are bright (sometimes fantastically so) and the females are dull and cryptic. The females look after the nest, so it would not be good for them to be bright. On the other hand, sexual selection acts to make the males ever brighter and more attractive. Sometimes the ridiculous displays of the males attract the attention of predators, though, so this selection must be balanced.
There are some animals where the trend is reversed, and these examples are very interesting in their ability to illuminate the reason for sexual dimorphism. For example, the Eclectus Parrot. The females are brightly coloured and the males are a cryptic green. The behaviour shows why: it is the male that looks after the nest while the female finds food.
You may argue that some human societies have also reversed this trend. The females are often brightly ornamented and males sometimes take charge of parental care.
Some have not reversed the trend.
The task of attracting a mate often goes both ways. Both the male and female choose. In this way, complex patterns of behaviour are developed: courting rituals, mating rituals, etc. Not to mention some really beautiful displays.