How does natural selection lead to evolution

Natural selection occurs as the most successful of a particular species pass on their genes while the less successful fail to mate, and undesireable genes die out. this causes evolution over time because if a larger sized animal is desirable for survival, then these animals will find more mates and the next generation will be slightly larger, and they will continue to mate with larger animals eventually causing a larger average size. this works with colours/patterns, intelligence, beak/mouth shapes, things like that.