The common ancestor animals initially live in the same habitat and continue to interbreed with each other so they remain genetically compatible. At some point something causes the group to split into two or more sun groups which become separated from each other by enough distance that there is less and less interbreeding between the two groups.
If that happens for long enough the random mutations that occur and are selected for by evolution add up and the species genetics become more and more different. If they remain separated for a long enough time the two groups will become so different they no longer can interbreed and are considered two different animals now.
Imagine a small mammal like a rat. If you took one group of rats and placed them in an environment with lots of rivers and lakes for a long time they might adapt to that kind of environment by say, developing webbed feet which make it easier to catch prey in the water.
Meanwhile if you took a different group of that same animal and put it in a forested area they might develop long sharp claws which makes climbing easier.
Over time more and more differences occur due to natural random mutations and add up.
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