As with peacocks, roosters (top) are brightly colored to attract mates, while chickens (middle) are dully colored to protect the eggs and young effectively. The same is true of mallard ducks (bottom).
Though the large, twisted antlers of this buck may get it caught and hinder its survival, this risk is "worth it" evolutionarily, because the buck with the biggest antlers wins a mate, and the big-antler genes are passed on to his offspring.
Up until now, we have discussed reproduction of an organism as resulting from traits that enable it to survive. For example, in a cold climate, lots of fur enables survival, which enables reproduction (which leads to these traits being passed on and becoming more common). This can be called "reproduction through survival." The ability to reproduce, however, also results from traits that are directly related to the ability to reproduce, but play no role in the survival of the individual organism. This is "reproduction through reproduction."
In evolution, having traits that help one survive is very important, but it is only important so that one can reproduce and pass those traits to the next generation. For this reason, traits that enable an organism to reproduce, without necessarily helping them to survive are selected for: the ones that reproduce pass the traits that helped them to reproduce on to their offspring and the ones that don't reproduce don't have offspring, so their traits disappear from the population. Darwin called this idea "sexual selection".
Here are two examples:
The male peacock has a lot of showy feathers. One would think that these would not appear in evolution; they would be noticeable to predators and would get the peacock stuck so it would not be able to escape from predators or get food. However, peacocks use their feathers to attract peahens (female peacocks). The peacocks with the showier feathers are able to attract mates, so they are the ones that have offspring, and pass on the fancy-feather genes to the next generation. However, the organism must also be able to survive. Peacocks can fold up their tails, which lessens the danger of being noticed by predators or getting caught in the bushes. In addition, as with most species where the males are colorful or fancy to attract the females, the peahens are much duller and more camouflaged, in a large part because they are the ones who guard the eggs and chicks. Survival of the next generation is very important.
Many plants have flowers that are pretty and brightly colored. This is because the brightest colors attract bees, butterflies, and other pollinators, which enable the plant to reproduce. If a flower is dully colored, it does not reproduce, and the dull color genes disappear from the population, whereas the plants with brightly colored flowers reproduce, so they gradually make up more and more of the population.