Natural selection is the phenomenon by which the nature selects those species which possess survival advantage over the other species. According to theory of natural selection, there is "struggle for existence" within the species of a population for the environmental resources and this struggle leads to survival of certain organisms and elimination of the less competent species. Thus, in this competition, some organisms might undergo genetic changes which help them in their survival. The better adapted organisms would, thus, survive and pass on their traits to next generation, gradually leading to evolution.
Speciation is a process of formation of new species from the existing one due to reproductive isolation of a part of its population. This reproductive isolation can occur due to geographical isolation of a part of population.
With time, the genetic drift will accumulate different variations in each of the geographically separated sub-populations. Ultimately, all the individuals of these two groups will isolate reproductively, thus, leading to formation and evolution of new species. Thus, we can say that both natural selection and speciation lead to the evolution of species on earth.