What cultural issues does Foucault shed light on in this book.

In Discipline and Punish, Foucault challenges the idea that the move from physical punishment to reforming a person through surveillance and psychological means—what Foucault calls discipline—is an "advance" from barbarism to a more civilized approach to treating criminality. Both are displays of power, Foucault contends, but what we today see as the extreme cruelty of physical punishment was, in former times, kinder than modern discipline. We have gone from punishing the body to controlling the soul. 
Foucault looks first at how criminals were dealt with in the Renaissance, pointing out that they were often tortured or killed so that the power of the king could be inscribed or shown on their bodies. Punishment, including execution, was a public spectacle, a display of power. However, while their bodies were physically punished in harsh ways, criminals' souls were largely left alone.
Foucault then turns to discipline and describes it as revealing the movement of power from the body of a king to the invisible power of the state. Now, criminals are both hidden away and subjected to endless surveillance. Foucault cites Jeremy Bentham's concept of the panopticon, a prison in which the prisoner was under constant surveillance, as the model for the new concept of discipline. Outward punishment was now no longer enough: the mind and soul of the prisoner also had to be kept in subjection. As Foucault put it:

It is the fact of being constantly seen. . . that maintains the disciplined individual in his subjection.

The important point is that Foucault reverses the idea dear to our culture that we have become more humane in how we treat criminals. By constantly observing the criminal and forcing him—and, in fact, all of us—to internalize the values of the state, we have become less free than we used to be.