Augustine recaps everything he has said so far, especially that God created mankind from two parents so that 1) we would all have the same nature and 2) we might be bound together "by the bond of peace... into one harmonious whole." And yet, because of sin death has appeared and become rooted in human nature. If not for grace, all of us "would have been hurled, by a just punishment, into a second and endless death had not some been saved from this by the gratuitous grace of God."
But, because some are saved, we can say that there really are only two "cities" in the world, despite the wide variety of "religion and morals, language, weapons, and dress." The city of man, which lives "according to the flesh" and is headed for destruction; and the City of God, which lives "according to the spirit and is bound for eternal life." Each city lives according to "its own kind of peace and, when they attain what they desire, each lives in the peace of its own choosing."
Again, we see the repeated theme that mankind is driven by love. In our natural state we love ourselves, sin, and death. Under grace, we love God. This is what at the end of the day divides man from man, and in a very real sense is the only division that actually counts.
But what does it mean to live "according to the flesh" as opposed to "according to the spirit"? We must not think of this in mere physical terms--"according to the flesh" does not mean we're condemning the Epicureans, who live only for their own stomachs (though we do condemn that). Nor does "according to the spirit" mean that we agree with the Stoics, who place the good of the soul above all other things.
Scripturally, "according to the flesh" means nothing more and nothing less than living according to human nature. In short, it is to live as if there were nothing higher or more important than man. In this sense, both the Stoics and the Epicureans live according the the flesh. Such a life is evidenced in the sorts of things Paul talks about in Galatians 5 (immorality, idolatry, etc). But! We must realize that such things are not just external, they are rather reflections of a sinful nature. When we remember that, then in some ways (as Paul talks about) even the virtues become signs of a sinful nature. For example, if a person believes that his idol has commanded him to be temperate in his diet, it might appear that he is exercising the virtue of self-control. Yet, even that virtue reflects the sinfulness of his heart, since he is doing it out of the wickedness of worshiping statues.
Living according to the flesh, then, is neither merely a practice of the body nor a delight of the soul, but rather both--an entire inclination of one's nature to embrace self-worship as the highest possible good. (The useful Puritan word for this is "affection", which includes--but is not merely--the idea of love.)