Natural selection is Darwin's great insight: the mechanism that turns blind variation into apparent design. It is startlingly simple, yet it accounts for the fit of living things to their world.
The logic
Selection follows from three facts already in hand plus one more. Individuals vary; some of that variation is heritable; and more offspring are produced than can possibly survive, so there is a struggle to survive and reproduce. Put these together and a conclusion is forced: individuals whose traits happen to suit their environment will, on average, survive and reproduce more, passing those traits on. Generation by generation the helpful traits become more common and the unhelpful ones fade. That is natural selection: "the survival of the fittest," where fitness means nothing more than reproductive success.
The peppered moth
A textbook case is the peppered moth of industrial Britain. The moths came in pale and dark forms, resting on tree bark. Before industrialisation the bark was light with lichen, pale moths were well camouflaged from birds, and dark moths were rare. As soot from factories blackened the trees, the tables turned: now the dark moths hid well and the pale ones stood out and were eaten.
Within decades dark moths dominated the sooty districts. When clean-air laws later lightened the bark again, the pale form recovered. The population's makeup tracked the environment, exactly as selection predicts.
No designer needed
The crucial point is that no one is choosing. There is no plan, no goal, no foresight: only differential survival among random variants, repeated over many generations. Yet the outcome looks designed: moths matched to bark, beaks matched to seeds, camouflage matched to background. Selection is a mindless sorting process that nonetheless builds intricate, well-fitted forms, simply by preserving what works and discarding what does not. Understanding that is understanding how the appearance of design arises without a designer, and it sets up the next question: just how far can this process reach?