When an individual animal in a species evolves, a new trait that helps them better survive in their given environment by making it easier to hunt or forage for food, survive against predators, persevere through rough climate, or any number of other tasks. The organism, in turn, has a higher chance to survive long enough to mate than other animals in their species without that trait. Over an extended period, more and more of the species will develop this trait because the individuals with the trait will more likely mate, therefore passing the characteristic onto their offspring who will also have a higher chance of survival; this continues until all of the species has the trait.
Through the process of natural selection, any individual that has a unique trait to their species that will increase their survival rate and can be passed down to offspring will eventually spread to the rest of the species. There are many challenges that a species may face whether it be a shortage of food, harsh weather, predators, disease, etc. These challenges may lead members of species to not make it to maturity to mate and produce offspring. Traits that individuals of a species develop that help them overcome one or multiple of these challenges that they may face will increase their chances of making it to maturity and producing offspring that will have a higher chance to survive till adulthood and pass on the trait.
An example of natural selection would be a species of wild cats who hunt mice for food and are prey to coyotes that live in the area. One of the cats develops larger ears, which allow the cat to hear the mice from farther away. This trait enables the cat to hunt better, which in turn dramatically increases its chance of making it to maturity to mate and pass it on to its offspring. As this process continues, more and more of the cats will have larger ears until the whole species of cats have larger ears.
As Charles Darwin (The creator of the natural selection theory) explained the theory to other scientists, he defended that this process could develop things such as the vertebre eye, which could be explained through a string of natural selection occurrences that develop advantages in the clarity of vision which would be passed through the species as it is a direct advantage over the less clear eye which came before. Through gradual evolution complex natural structures could be formed.