How is the peppered moth of England an example of natural selection?

The peppered moth had white bodies and wings, peppered with black. This coloration blended well into the original British countryside, hiding them from their predator the birds. Factories of the early industrial revolution covered everything with soot. Now the white stood out against the black surroundings making them easy targets for birds. Over time the white moths were wiped out. But, a few of them were darker in color, these survived and multiplied such that the white peppered moth was replaced buy the dark ones.

Black moths were selected for when the trees turned black.

the moths with the high fitness were selected for

The black moths were more fit for survival, so their phenotype frequency increased.