In the beginning of the section on extinction we find an amusingly extreme understatement: "Rarity, as geology tells us, is the precursor to extinction." But this is followed by a comment to the effect that the fluctuations in population size will make smaller populations are more likely to go extinct than larger ones: and the same could be said of allele frequencies in genes, which is a respelling of the concept of genetic drift. Darwin could have gone so much farther with that idea, but it is impressive that he got as far as he did. Darwin's point here appears primarily to be a reminder that extinction is a real phenomenon, and to reiterate and emphasise his earlier point, that competition between very similar species is the most severe. I am not sure whether this is in fact the case, but if so, it gives a nice mechanism for the quick and clean separation into different species of differently constituted but overlapping populations of the same species.
The next section, on "Divergence of Character", is an effort to explain how the slight differences between populations can become the stronger differences between species. He strikes analogy again with artificial selection: breeders, when selecting from amongst their charges, will choose those individuals most characteristic of the breed in question, which will tend to be the more extreme in those traits when compared to the wild stock. The point here is that selection acts continually over a long period in the same direction, and exaggerates those traits which it selects. Because of this, local populations become specialised. This results in another phenomenon that he notes next, that invasive species (to use the modern term) tend to come from different genera from those of the native populations: they have evolved from dissimilar species to fit similar niches. He draws an analogy between different species in an ecosystem to different systems in a single organism, thereby anticipating the Gaia hypothesis! On a more respectable front, however, looking at the analogy from the opposite direction offers a description of the evolution of multicellularity, in which early organisms were largely homogeneous, and easily outcompeted by those organisms whose cells started to specialise.
At this point Darwin introduces us to the only diagram in his book, which is also almost an early cladogram. Darwin takes some trouble to explain it; to those of us used to reading cladograms, it offers nothing new, but he offers more than cladograms do here as well. In this diagram, unlike in cladograms, the horizontal axis has meaning. It is well-designed for his purpose, as it simultaneously demonstrates diversification, extinction, and the varying genetic relationships between descendants that we now call phylogeny. He also touches on an important point made by Stephen Jay Gould in Wonderful Life, that the history of life is not one of increasing diversity from a small group of ancestors, but one of pruning of radically different branches of the tree and their subsequent replacement by radically different descendents of the few survivors. Darwin posits that life becomes more varied over time, but here he is not necessarily correct: in some ways (as Gould points out) the variety of life diminishes as time goes on and fundamentally different lineages are wiped out. While the surviving lineages may diversify, even into niches unoccupied by the previous assemblage, they are built on fewer platforms than at one time existed.
Darwin concludes the chapter with a summary, which offers nothing new, aside from an explicit description of a concept that is still current, that of the Tree of Life. While this has come under attack of late (endosymbiosis and gene transfer between unrelated groups providing two significant challenges), it is still a useful metaphor -- especially so in macroscopic organisms. Darwin also employs some very nice language. To give an example: "It is a truly wonderful fact -- the wonder of which we are apt to overlook from familiarity -- that all animals and all plants throughout all time and space should be related to each other in group subordinate to group…." And another: "As buds give rise by growth to fresh buds, and these, if vigorous, branch out and overtop on all sides many a feebler branch, so by generation I believe it has been with the great Tree of Life, which fills with its dead and broken branches the crust of the earth, and covers the surface with its ever branching and beautiful ramifications." Darwin is not done yet with the fundamentals of this theory, but he has still managed to encapsulate its essence admirably.