What is the main idea of Darwin's theory of evolution by natural selection?

Darwin's theory of natural selection is as follows:

Darwin observed that population sizes of any species would increase exponentially if all its individuals born reproduced successfully.

However, Darwin observed that populations tend to remain the same size (except for seasonal fluctuations).

Darwin also noticed that resources are limited.

Thus, Darwin concluded that if more individuals are produced than the environment can support, then there is a struggle for existence among the population's individuals, and only some of the offspring survive each generation.

Darwin also observed that no two individuals are exactly alike.

As a result, Darwin concluded that individuals whose inherited traits give them a higher fitness (a higher probability of surviving and reproducing) and are more likely to leave more offspring than less fit individuals; survival depends on inherited traits.

Darwin then inferred that favorable characteristics will accumulate over generations as this unequal ability of individuals to survive and reproduce will eventually lead to a gradual change in population, especially as environmental factors filter heritable variations.

Furthermore, he realized that much of this variation is heritable. Darwin's theory can also be explained as natural selection, the differential success in reproduction among individuals that vary in their heritable traits, emerges as each individual interacts with its environment. Over time, the adaptations of organisms to their environment will increase due to these reproductive differences. Then, if individuals of a particular species move into a new environment or if the environment changes, natural selection does result in adaption to these new conditions, while regularly & occasionally giving rise to new species. Note that a population is the smallest unit that can evolve, natural selection can increase or decrease only heritable traits, and the favored traits depend on the environment.