In the given case, if the trait is favorable, it will be passed on to the offspring over many generations, leading to a population of darker squirrels.
The mutation refers to the sudden modification in the DNA's nucleotide sequence. Some of the mutations are harmful, while some offer survival benefits to the species. The mutations that offer the adaptive or survival advantages are favored by natural selection and the species with this kind of mutations seem to reproduce and survive more in comparison to the species with no mutation.
Therefore, if the darker color fur would be beneficial to the squirrel, for example, it would be tough for the predators to locate the squirrel with darker fur, then they seem to survive more and the traits keep on passing from one generation to another.