Retribution is perhaps the most intuitive - and the most questionable - aim of punishment in the criminal law. Quite contrary to the idea of rehabilitation and distinct from the utilitarian purposes of restraint and deterrence, the purpose of retribution is actively to injure criminal offenders, ideally in proportion with their injuries to society, and so expiate them of guilt.
The impulse to do harm to someone who does harm to you is older than human society, older than the human race itself (go to the zoo and watch the monkey cage for a demonstration.) It's also one of the most powerful human impulses - so powerful that at times it can overwhelm all else. One of the hallmarks of civilization is to relinquish the personal right to act on this impulse, and transfer responsibility for retribution to some governing body that acts, presumably, on behalf of society entire. When society executes retribution on criminals by means of fines, incarceration or death, these punishments are a social expression of the personal vengeance the criminal's victims feel, rationally confined (it is hoped) to what is best for society as a whole.
Of course there are more sophisticated ways of thinking about retribution, and it's a good idea to be familiar with them since a judge (and that other kind of judge, the criminal law professor) is unlikely to accept "because it's a natural impulse" as justification for retribution in punishment. And with good reason.
While "it's natural" tends not to carry much weight in the criminal law, "it's morally right" can. Moral feelings and convictions are considered, even by the criminal law, to be some of the most powerful and binding expressions of our humanity. In binding criminal trial juries to restrict guilty verdicts to situations of the highest certainty, "beyond a reasonable doubt" is also often described as "to a moral certainty." It is to their moral feelings of what is truly right that jury members are asked look before delivering a verdict. It's perhaps not too much of a stretch, then, to argue that it's morally right to make criminals suffer as their victims have suffered, if that's the way one's moral certainty points.
No matter what one's moral feelings are about inflicting deliberate harm on a human being, the majority of the U.S. citizenry still holds that it's right to exact retribution on criminal offenders, sometimes even to the point of death. This is almost certainly true of the majority of victims, and their loved ones, for whom equanimity becomes more and more difficult depending on the severity of the crime. What rape victim does not wish to see her attacker suffer? What parent does not hate the one who killed their child? The outrage that would result from leaving these passions for revenge unsatisfied might be seen as a dramatic failure of the entire criminal justice system. It's a good argument for retributive justice, then, that in this world public vengeance is necessary in order to avoid the chaos ensuing from individuals taking revenge into their own hands. And, until the moral certainty of a majority of society points towards compassion rather than revenge, this is the form the criminal law must take.