What is the relationship between evolution and natural selection?

Natural selection influences and directs evolution by only letting the organisms with the best traits survive. For example if some elephants migrated to Siberia and some had traits for extensive body hare natural selection would usually only let those elephants survive since its cold in Siberia. This would then lead to the elephants evolving into woolly mammoth type creatures or something entirely different. Basically natural selection only lets organisms with the best traits survive thus setting a path for the evolution of that species.

Natural sletion is the idea that the fittest survive and pass along there traits to there offspring evolutuion is that we evoleved from a single cell organism then so on and so on