You are probably talking about mate choice or intersexual selection. This evolutionary strategy helps animals find the healthiest and most rigorous individuals to pass their genes onto. In animal world, attractive appearance and confident actions are traits of better genes. A mate with characteristics like vibrant plumage and better courtship actions is more likely to be healthier and more likely to produce healthy offspring. It also means that the pair, or the mother, have better chances of reproducing.
Answer: Intersexual selection
Sexual selection is a process in which an organism survival and reproduction is favored by it's phenotypic traits. The one organism having better phenotypic trait will be able to attract members of opposite sex in order to copulate and reproduce new organism. Here, the attractive feathers in male peacock is a useful phenotypic trait to attract female mates is an example of intersexual selection.