Natural Selection is actually the process through which the favorable heritable characteristics get more common in coming generations of a population of reproducing organisms. The unfavorable heritable characteristics become less common in the next generations. This happens because of differential reproduction of genotypes. Natural Selection process acts upon the phenotype, so that the favorable phenotypes are more likely to survive and reproduce.
On the other hand, Artificial Selection is the process of intentional breeding of certain characteristics in the coming generations. It is also known as selective breeding. The genetic process in artificial and natural selection is the same. However, in artificial selection the human preferences have a significant effect on choosing the favorable traits that are bred further.