A general theory of punishment which advocates the infliction of pain on the offender which is commensurate with the crime. Possible reform of the individual or future deterrence of crime is not a reason for punishment.
Utilitarianism
A general moral theory which states that one's actions should be guided by a principle which produces the overall best outcome to all of those affected by one's actions. In the issue of capital punishment, utilitarians may justify capital punishment on the grounds that it does produce the overall best outcome by deterring crime and/or by rehabilitating the offender.
Moral vs. Legal Wrongs
Legal wrongs are wrongs which violate existing laws of the society. Committing a legally wrong act does not necessarily mean that one is committing a moral wrong since some laws might be immoral. Also, committing a legally correct act does not necessarily mean one is also committing a moral act. So, it could be the case that capital punishment is legally correct but morally incorrect.
Description vs. Prescription
To describe things is to tell how things are. To prescribe things is to say how things ought to be. In the context of capital punishment, one might simply describe how capital punishment is administered and how often it takes place, but prescribing capital punishment is to say that it ought to take place.
Context
While capital punishment has been used by different societies for thousands of years, it is not today universally accepted.
Key Questions
Is capital punishment morally justifiable?
Since many other forms of punishment such as life-imprisonment are available, why should capital punishment be used at all?
What can capital punishment accomplish that cannot be accomplished with life-imprisonment?