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.
