This is basically about what he calls the “commitment theory” of why people behave the way that they do (and not as economists generally suppose.) This is basically:
Generically, he considers “commitment problems” to be situations where we benefit from somehow committing ourselves to potentially behave against our self-interest at some times in the future. An example he offers which is I think more relevant that prisoner's dilemma (though logically equivalent) is two people who start up a restaurant, one who is a good cook and the other who is a good businessman. They gain a benefit by working together, but each is also faced with numerous opportunities to cheat, such as by stealing from the till or taking kickbacks from suppliers. How can they trust each other, and indeed, how can they trust themselves not to give in to the temptation?
The fact that emotions regulate our behavior is the key to solving the problem. First, emotional expression is involuntary and difficult to control. This means that emotion is a difficult-to-fake signal. It benefits you to make emotional displays appropriate to the situation because it communicates your character to others. We believe that we can judge the character of others, and probably we are right fairly often. Experiments have shown we have some ability to detect deception via nonverbals.
One idea that he proposes, though doesn't really support, is that “character” is real, that it is not natural to be highly opportunistic, to be honest when people are watching and cheat when they aren't. The best way to come across as honest and trustworthy is to work at being honest and trustworthy, even when nobody is watching. Reliable emotional signals could evolve because of the benefits trustworthy people gain by working together. By spending enough time and effort, we are able to fairly accurately judge how trustworthy people are, but due to the cost you reach an equilibrium where there is a small number of cheaters in the population. As long as the number of cheaters remains small, it isn't worth the effort of trying to detect them. He also develops the compatible alternate theory that the social emotions are the primary means of self-control. A reward here and now is very compelling (hyperbolic discount function), so we must set a powerful emotion against this. This leads to a story about why reputation is important. You might supposed that clever cheaters would only cheat when they aren't likely to be caught. But if you believe that difficulty with self-control is the main cause of cheating, then it is likely that cheaters will not be so clever in practice, and will be caught, getting a bad reputation.
As Dennet put it, in discussing this book in Freedom Evolves, actually being good is a hard-to-fake signal that you're good.
He then goes into several chapters looking at different scenarios and the associated emotion, showing that people don't in fact behave in a self-interested way with respect to fairness (compensation levels, dictator game), love (exchange model has power, but doesn't describe the subjective experience of mate selection), human decency (good Samaritan, etc.)
w.r.t. Fairness, the only group that played the dictator game at all as economists would predict were economics grad students. Also, interesting to note w.r.t. Status, that economists have puzzled over the fact that pay scales seem much flatter than the actual variation in productivity. It seems that in effect that the status in the firm has monetary value, and that high producers are willing to sacrifice pay in exchange for status. Or to put it another way, the high producers are willing to pay the low producers extra just to hang around and make them look good by comparison. And individuals can perhaps choose their status at a given productivity level by choosing firms with higher or lower productivity. That is, the “big fish in a small pond”.
He's an economist, and is more or less writing to economists, so his main concern is in showing that people don't actually behave in the self-interested way that economists suppose. This is a deeply intuitive result to normal people, so is not particularly interesting to a general audience, though perhaps there's enough cynicism and “world-is-going-to-hell-in-a-handbasket” concern that some of these good news results would be useful. I guess it's also valuable to argue that you can take a scientific/evolutionary viewpoint without any compulsion to view self-interested behavior as normal or appropriate, and without dismissing altruism as illusory or cynically self-serving.
What I think is more interesting is the story that emotions are “reasonable.” (Stefan Heck, Reasonable behavior: making the public sensible, in Damasio) Emotions influence us as they do for good reasons, and there is a plausible story of how the could have evolved.
Also, “bad” emotions such as anger at unfairness or angry desire to punish a transgression are also broadly adaptive because of their deterrent value. Punishing is not rational because it incurs a cost and possible serious risk to life, often without any real expectation of getting compensation. But if you can get a reputation as someone not to mess with, that is beneficial in the long run. I note also that punishing cheaters benefits the entire honest population by discouraging cheating in general.
The idea of emotions as a support to self-control also ties in very well with the idea that Damasio advocates, which is that emotions seem essential to good judgment, and that people whose social emotions have been impaired are quite unable to function in society even though they don't seem to have any cognitive deficit. They don't understand the seriousness of the consequences of their actions.