How do natural selection and adaptation play a role in evolution?
A very important role in determining which organisms have the best biological adaptations to survive in a given climate.
Natural "selection" is a bit of a misnomer, as no one or thing actually does any "selection" per se. But those features that give an organism the most chance of living, reproducing and passing on their genes to the next generation get "selected" and those that don't have these optimal traits gradually die out.
For example, in our own primate evolution long fingers were adpative for life in the forest. But when the climate changed in East Africa, long fingers still had some usefulness, but being able to walk upright became more adaptive and allowed early humans to run after game, see predators over the grass, etc. Fingers became a bit shorter. So, those that had the upright set of genes continued to thrive and survive and those that did not, slowly vanished.