We must not, like the Gnostics or the Manicheans, think that sin comes from the flesh. Rather, the flesh is sinful because the soul is sinful. "For the corruption of the body, which is a burden on the soul, is not the cause but the punishment of Adam's first sin. Moreover, it was not the corruptible flesh that made the soul sinful; on the contrary, it was the sinful soul that made the flesh corruptible." We know this is true because the devil shares all the same sins that we do (albeit in greater form), yet has no flesh himself.
But what it is this sin of the soul? It is living to man rather than to God. "When man lives according to himself, that is to say, according to human ways and not according to God's will, then surely he lives according to a falsehood."
When we define ourselves as the chief end of our own being and existence, we find that we have fallen into sin. Our goal in living is always [as even the pagan Aristotle noted--no, Augustine doesn't point this out, but I'm teaching on Aristotle in the fall and it keeps coming up] happiness. "Man indeed desires happiness even when he does so live as to make happiness impossible."
This is one of the aspects of sin, and "the reason why every sin can be called a lie." It promises happiness while dividing us from the very source of happiness Himself--God. "For, when we choose to sin, what we want is to get some good or get rid of something bad. The lie is in this, that what is done for our good ends in something bad, or what is done to make things better ends by making them worse." We pursue goodness, because we know that virtue leads to happiness, but we pursue it in ourselves rather than in God, and so we get neither goodness nor happiness despite our best efforts at it. Hence we have two cities, the city of man which tries to find happiness within creation; and the city of God which tries to find happiness through faith in the Gospel. Again, we must not think of pursuing fleshly desires in a strictly carnal sense, but rather must realize that man as a whole being--spiritual and physical [if the word hadn't been appropriated by worse theology, we could say man as an "existential whole"]--is involved in this pursuit of happiness through sin and rebellion.