Sexual selection means some individuals are more successful than others in reproduction based on heritable traits that are not adaptations to the environment but that give them an advantage when they breed.
For example, sexual selection in the chimpanzee has resulted in the increase in the size of the penis. A longer penis is not needed for the struggle for survival but it gives the chimp that has it a greater chance of impregnating a female, because chimpanzees are promiscuous, and a female may mate with many different males, A longer penis allows a chimp to place sperms closer to the uterus than those that have been left by other males with shorter penises. Chimps also have large testicles to store lots of sperms. They allow the male to place more sperms into the female so that one of them has a good chance of fertilizing the egg. Since long penises and large testicles are not traits that are needed for survival, they are considered products of sexual selection and not natural selection.
The male peacock's feathers do not appear to be needed for survival at first glance. It has been theorized that they are also products of sexual selection, because it is thought that females are attracted to males with large and colorful tail feathers and prefer them over males with smaller and/or less colorful feathers. it is ASSUMED that the large tail feathers make male peacocks more conspicuous and therefore more likely to be eaten by predators.
However, there is one study that questions this theory, because in that study, it has been shown that females actually are more likely to be eaten than males. It may be because the male peacock's tail feathers, which have a lot of eyespots, can actually frighten away predators. Lots of animals (such as fish, cobras, caterpillars, and butterflies) have eyespots on their bodies and these evolved to scare away predators, because the eyespots fool animals into thinking that a large powerful predator is present. Even if the peacock's feathers may not be the product of sexual selection, sexual selection does exist and it can result in the evolution of body parts that otherwise would not evolve. The gorilla for example have a much smaller penis than the chimp because gorilla males exclude other males from mating with his harem through strength and combat. Male chimpanzees OTOH band together as a troop so they cannot afford to fight each other over the right to mate. Instead they engage in a secret war of the penis to decide who can father the most young. Such competition has resulted in the evolution of a larger penis than the gorilla's.