How does adaptation evolve?

Because if the adaptation is usefull or essential to the survival of a species then only the animals with that adaptation will get offspring and therefore more and more animals are going to have the adaptation.

For example the color of the coat by mice. If one mouse has a diffrent color than the other mice but his color matches their environment more than the coat of the other mice he is less likely to be seen by predators and therefore survive longer and get more offspring.

There is a theory that is called "natural selection" of "survival of the fittest" you should look it up for a better/longer explanation