Alright, ftv, so that's what ToE says about one of the main ways we get a new species. So what we see is that the new species branches off from an existing species, is not very different from that existing species, and comes into existence in a very understandable, not-mysterious way. You don't have to understand mutations; Darwin had no idea that DNA even existed. We all know that offspring resemble their parents, but not exactly.
So that's a huge piece of the theory. The second big piece is just the idea that another new species can arise from the new species, and another new one from that, and so on. That this is the way all new species come into existence, in a continuous, ongoing process.
So you'll never see a dramatic kind of change. Every change will be gradual and subtle, and grade gradually into a new species. Yet over a very long time, gradually, dramatic differences will emerge. Eventually Biologists have to call a new species a different family.
So ToE says that's not only how we get new species, but new genii, families, and so forth.