What is the book about? Schelling sums it up best himself, on p.13 (emphasis in the original):
What this book is about is a kind of analysis that is characteristic of a large part of the social sciences, especially the more theoretical part. That kind of analysis explores the relation between the behavior characteristics of the individuals who comprise some social aggregate, and the characteristics of the aggregate.
Schelling is very good at expressing mathematical models in ways that make them relatively easy to understand. That is not to say that you will understand them if you don't understand basic mathematics (especially algebra), only that people who do understand basic mathematics will quickly pick up the ideas that Schelling is putting forward.
There are a number of contributions that this book makes, that are interesting to the general reader. The first is how people sort or segregate themselves, and may do so based on very weak preferences for not being in the minority. This idea (the so-called checkerboard model of segregation) has underpinned a lot of interesting empirical research on ethnic segregation (which one of my PhD students is currently working on as well in a study of ethnic diversity in Auckland). The second contribution is about how people's choices are influenced by the choices of others (as represented by population-level totals or averages). Do you prefer to do the same things as others, or different? The third contribution is analysis of the multi-person prisoners' dilemma, where the payoff to each player in the game depends on the choices made by many others (recall that in the standard prisoners' dilemma, there are only two prisoners). This contribution defies a simple exposition, so I encourage you to read it for yourself.
I also found this bit interesting (in relation to choosing children's genes):
IQ might be treated as a competitive trait; valuable as it may be for its own sake, it may be construed particularly valuable in a competitive society, whether the competition is based on IQ measurements themselves, on the school success to which IQ may contribute, or on competitive success in one's career. If it were widely believed that the genetic mixtures within most parents made it possible by chromosomal selection to raise the expected IQ of a child by many points above what it would have been by chance selection of the chromosomes; and if it became widely believed in certain social classes that nearly everybody was taking advantage of this opportunity; parents might feel coerced into practicing selection not out of any dissatisfaction with the prospective intelligence of their children, but to keep up with the new generation.
This is really interesting since I think it links to Robert Frank's ideas of competition at least in the short term (see for example here) - while the resources necessary to choose children's genes to select for higher intelligence (or alternatively for other desirable physical traits) are scarce (and costly), this is an option that is only available to the wealthy. And only a few genes might be targeted. The middle class then might desire similar selection for their children, and demand increases. To keep their relative advantage in the gene selection process, the wealthy might select on even more genes (a more costly process), and so on. Some food for thought anyway.
Overall, as I noted above this book has aged really well, is still very relevant to many things, and is definitely worth a read.