If a mutation ends up being beneficial to the survival of a species, then the likelihood of survival is greater. If those changes accumulate over successive generations in a population of a species, that is a change. If those changes result in a population no longer being able to produce fertile offspring with other populations, then speciation has occurred.
If we take an organism, let's called it a gyullip, and the gyullip lives in a forest of dark oak trees where its dark coloration makes it harder to be seen by predators then it is more likely to live long enough to mate and pass on its genes to the next generation. Mutations happen which means that not every gyullip is exactly identical to the next, some are slightly larger some are slightly smaller, some are born with a white coloration due to a mutation in their genes. These white gyullips are easy prey because they stand out on the dark oak trees, they are rare and rarely live long enough to find a mate.
Now the dark oak gyullip forest over time starts to disappear, a parasitic organism has been introduced into the area that slowly kills the roots of the dark oak trees, and over many years the forest begins to disappear--however the smaller white birch trees aren't affected by the parasite and where where the dark oaks used to stand the birch trees have begun to thrive, slowly replacing the dark oak forest with a white birch forest.
As the dark oak forest has disappeared, the dark colored gyullips have been having a harder and harder time surviving, competition over food, the dark oak trees, and over predation has lowered their numbers. However, remember the rare white gyullips? Well they were easy prey in the dark oak forest, and so that gene expression almost always resulted in the death of the gyullip. However white gyullips have been fairing far better with the new white birch trees, and so a split in the population has taken place--where the birch trees have come to dominate white gyullips are more plentiful and where there are still dark oak trees the dark colored gyullips have remained more plentiful. And so a natural separation of the two populations has occurred, and as such dark gyullips mate with other dark gyullips and white gyullips mate with other white gyullips, and these two populations of gyullips exist where there was only one before.
Now, of course, the white coloration mutation isn't the only mutation--as of course not every gyullip is identical to the next, there have always been various differences, some are smaller some are bigger as noted. There are also many mutations without an outward observable result. Slight changes in the chromosomes, or slightly different shaped proteins being made in the cells.
If the two populations, over time, are no longer capable of mating and producing fertile offspring together, we have speciation. Perhaps the white gyullips have also been getting smaller over generations because the smaller birch trees means larger white gyullips have a hard time competing for food and so smaller white gyullips had better opportunity to successfully mate and pass on their genes.
That, in an extremely over-simplified way, is natural selection and how it results in changes over time and can result in new species.
These things aren't just said to have happened,
we observe these things happening.
https://evolution.berkeley.edu/evolibrary/news/100201_speciation
https://news.nationalgeographic.com/news/2008/04/080421-lizard-evolution.html
https://askabiologist.asu.edu/peppered-moth
-CryptoLutheran
