A lot is said in this section, and Darwin tries to put forth a solid basis for his reasoning that variation leads to speciation by giving a conceptual example.
He suggests that if we look at a given point in time, we may have eleven different species within a single genus, "large within its own country" - i.e. there are many different species and much variation within each species of this genus in a given area.
If we imagine that two of these species vary a lot, and produce, after many generations several varieties each, and these in turn produce multiple varieties, and so on up the ages. While at the same time most of the other species in that genus die off - possibly because the two which are varying a lot are doing so because they have some advantage, and start to occupy the niches that the other species were. And because they have this advantage, they perform much better than the other species that are not varying quite so much, and not producing offspring that can survive quite as well. But still these two species' offspring are also competing amongst themselves, and of course some of the varieties die off...
After many thousands of generations, we might have eight variants of the first species, and six of the second species, and perhaps one of the original 11 species manages to survive through that many generations, also, but relatively unchanged. From Darwin's diagram on pp. 160-1 we can see that from the one species (A), out of the eight variants that have made it through, one group of three is fairly closely related, another group of two is also closely related, and a further group of three is closely related. We can also see that the latter group of three is more distantly related, and hence more distinctly different to either of the first two groups.
A similar situation exists in the second species' (I's) progeny. We have two groups, each consisting of three very closely related varieties each.
We can also see that these two groups will be quite distinct from each other, for not only were the ancestors whose progeny they are somewhat distinct, they have also accumulated differences as the ages pass.
What's more, they are each somewhat closer to the species that descended from the other species, F, than they are to each other, by the fact that species A was more distinct from I than it was from F, and the accumulated variations are less likely to have brought them closer together than further apart.(*)
He then goes on to point out that a naturalist looking today at the varieties would most likely lump the three groups descended from A into three separate sub-genera or genera, and likewise those of the descendants of I....In other words, they are separate species.
(*) At least - I think this is what he is trying to say. I am not 100% convinced on this front, although I can see an argument for saying that the number of ways of diverging are greater than the number of ways of converging, thus statistically they are more likely to diverge than converge.
After reading this chapter, I can still see how a creationist might claim that Darwin has not proven that speciation does actually occur. My other thought is that he is relying on variation which he has stated stems from sexual reproduction on which natural selection can then work. If we start with a single single-celled organism produced by abiogenesis, where does the variation come from? I guess we are relying on imperfect copying creating sufficient distinct entities quickly enough that natural selection eventually has something to work on.