Blackstone had argued that the power of pardon was one of the advantages of monarchy over other forms of government because it (1) reduced the temptation of courts to strain the interpretation of law in order to take into account all the circumstances; (2) endeared the Crown to the people through acts of compassion; and (3), although this is only suggested in passing and is perhaps not Blackstone's own view, allowed the prince to express in a subtle way its disapproval of a too-strict law.
Blackstone argues that a democracy can't seriously allow the power of pardon because there is no authority higher than the legislature and it would be inappropriate to give judges this power; which is fine as an argument as long as you don't have the tertium quid of an 'energetic magistrate' who is neither legislator nor judge. The colonies had carried over the power of pardon, and when they formed the Office of the President, the one that we know, they had two models to choose from: in most state constitutions the power of pardon was invested in the governor, in a few in the legislature. The power of pardon was given to the President in order to provide a check and a balance against Congress.
It's important to note that the power of pardon was not given in order to facilitate law or judicial justice. Quite the opposite; it was designed, and defended, on the basis that there needs to be a protection even from law and even from judicial justice. It was not made in order to prevent the backfiring of justice; one of the types of cases for which it was explicitly considered was the one where legal justice succeeds: the law was in general a reasonable one, and the judgment in court was a reasonable application of the law. As I think Oliver Wendell Holmes somewhere put it, it was explicitly supposed to include cases where policy required "a remission of a punishment strictly due, for a crime certainly ascertained." The cases where pardon can correct faulty justice were merely considered an additional benefit.
Hamilton explicitly argues that the power of pardon should be open to a very liberal use:
Humanity and good policy conspire to dictate, that the benign prerogative of pardoning should be as little as possible fettered or embarrassed. The criminal code of every country partakes so much of necessary severity, that without an easy access to exceptions in favor of unfortunate guilt, justice would wear a countenance too sanguinary and cruel.
It is thus entirely different from an acquittal; it does not imply innocence or vindication. Thus when we consider how it might be improved (and it is always possible that any clause of the Constitution might be improved), it does not make much sense to consider it as if it were part of the justice system. It is entirely a different matter: it is a distinct system for protecting people from the legislature and the courts; it is based on the principle that these things may not have a good result even when working quite well. (That there is some wisdom to this is seen in the aftermath of the Civil War, since Lincoln spent an immense amount of time using his pardoning power to protect deserters, especially very young ones, from full punishment.) Pardon is part of our justice system in a kind of incidental way; as it is set up to work, one can argue, it is (so to speak) part of our benevolence system, and works on the principle that mercy can and should sometimes supercede the ordinary operation of justice. James Wilson puts this point nicely:
The most general opinion, as we have already observed, and, we may add, the best opinion, is, that, in every state, there ought to be a power to pardon offences. In the mildest systems, of which human societies are capable, there will still exist a necessity of this discretionary power, the proper exercise of which may arise from the possible circumstances of every conviction. Citizens, even condemned citizens, may be unfortunate in a higher degree, than that, in which they are criminal. When the cry of the nation rises in their favour; when the judges themselves, descending from their seats, and laying aside the formidable sword of justice, come to supplicate in behalf of the person, whom they have been obliged to condemn; in such a situation, clemency is a virtue; it becomes a duty.
It's pretty clear, I think, that this in itself unsettles people; and repeatedly one finds that many of the arguments for restricting the pardoning power boil down simply to the fact that justice was not served. That really implies that there should be no real pardoning power at all; pardon gets its strength precisely from the fact that it is able to do this. The more restricted motivation that provides grounds for restricting the pardoning power (rather than eliminating it) is to discourage corruption. Certainly restrictions of the power to pardon are not unheard of -- the President perhaps has a less restricted power of absolute pardon than the British monarch had in the time of Blackstone. The pardoning power was (as I understand)in a way smuggled through the Constitutional convention, being added at the last minute and not discussed at length, despite being controversial; and it has, moreover, a long history of being used for political expediency. There is room for both motivations, if reasonably unfolded (as well as for reasoned defenses of keeping things as is, if any are on offer).* But I think it is very important to keep the two arguments distinct; otherwise we'll just make a hash of things.
* I'm of the view that the pardoning power is very important, and should be used more systematically than it usually is. I am open to arguments, however, that it could be reworked in ways to reduce any encouragement to corruption that might possibly result from it.
ADDED LATER: The blogosphere is abundant beyond all imagining. It turns out there is a blog devoted to the pardon power, both federal and state, by an expert on the subject.