A genotype determines the phenotype. The phenotype that is best adapted to the environment will be chosen by natural selection to survive hence survival of the fittest.
For an example take a genotype with two different recessive genes.
There are four possible phenotypes in a ratio of 9:3:3:1. If one of the recessives is for blonde hair and another for blue eyes, one 16 offspring will have both recessives. 3 of the 16 will have blue eyes and 3/16 will have blonde hair. While 9 of the 16 will have the dominate brown hair and brown eyes.
In the cultural environment of the United States the blonde blue eyed female will have a better chance of getting a mate and hence has a survival advantage to reproduce. The genotype has given rise to a phenotype that has an environmental advantage.
If we are talking about foxes in the arctic the fox with the blonde hair double recessive has a survival advantage over the brown haired fox. After multiple generations only the genotype that has the blonde hair recessive will exist in the genetic pool of the population. The brown hair genotype will become extinct in the environment.
Natural selection will lead to genetic drift toward the genotype that codes for the best adaptation for the environment. Natural selection can also lead to extinction of genotypes not well adapted to the environment. This is survival of the fittest. Natural selection can not create variations in the genotype it can only remove those that are poorly adapted.