This question strikes at the core of LDS doctrine - Christ's Atonement. Excuse my hyper-compulsive inlining of scripture references in my answer, but this is one of my favorite topics. I hope the reader will read the full text of the chapters I cite, as they explain it way better than I ever could.
The purpose of the final judgment is to be brought back into the presence of our Maker (2 Nephi 2):
10 And because of the intercession for all, all men come unto God; wherefore, they stand in the presence of him, to be judged of him according to the truth and holiness which is in him.
2 Nephi 9 explains further that everyone must stand before God, even if they are to be cast out:
15 And it shall come to pass that when all men shall have passed from this first death unto life, insomuch as they have become immortal, they must appear before the judgment-seat of the Holy One of Israel; and then cometh the judgment, and then must they be judged according to the holy judgment of God.
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22 And he suffereth this that the resurrection might pass upon all men, that all might stand before him at the great and judgment day.
So you might say that the purpose of the resurrection is to enable us to be in the presence of God. And this is very important.
Why? Because with mortality, we are subject to two deaths, physical and spiritual:
10 O how great the goodness of our God, who prepareth a way for our escape from the grasp of this awful monster; yea, that monster, death and hell, which I call the death of the body, and also the death of the spirit.
Death of the body is physical death, and death of the spirit is separation from God (rebellion, sin, etc).
The Atonement saves us from both deaths:
12 And this death of which I have spoken, which is the spiritual death, shall deliver up its dead; which spiritual death is hell; wherefore, death and hell must deliver up their dead, and hell must deliver up its captive spirits, and the grave must deliver up its captive bodies, and the bodies and the spirits of men will be restored one to the other; and it is by the power of the resurrection of the Holy One of Israel.
Thus, the resurrection redeems us from physical death, and the final judgment crowns our salvation from spiritual death:
15 And it shall come to pass that when all men shall have passed from this first death unto life, insomuch as they have become immortal, they must appear before the judgment-seat of the Holy One of Israel; and then cometh the judgment, and then must they be judged according to the holy judgment of God.
But why a judgment? Couldn't this all happen implicitly with the resurrection? Not really. Remember that there was a law given and it must be fulfilled:
16 Now, repentance could not come unto men except there were a punishment, which also was eternal as the life of the soul should be, affixed opposite to the plan of happiness, which was as eternal also as the life of the soul.
17 Now, how could a man repent except he should sin? How could he sin if there was no law? How could there be a law save there was a punishment?
18 Now, there was a punishment affixed, and a just law given, which brought remorse of conscience unto man.
So the judgment also has a practical purpose. It stirs up our minds and hearts to repentance.
14 Wherefore, we shall have a perfect knowledge of all our guilt, and our uncleanness, and our nakedness; and the righteous shall have a perfect knowledge of their enjoyment, and their righteousness, being clothed with purity, yea, even with the robe of righteousness.
Finally, the judgment is essential to our salvation, for without it, we could not be saved, even if we were really, really good. Without a judgment, there would be no law, and without the law, there's no standard against which to judge what "really, really good" is. So the law and judgment is a contract as much on our side as it is against us, depending on our choices.
And it would only condemn us if Jesus had not satisfied the demands of justice. But He did, so He can mete out mercy. And that mercy can only be had if there is justice, a law, and a judgment:
22 But there is a law given, and a punishment affixed, and a repentance granted; which repentance, mercy claimeth; otherwise, justice claimeth the creature and executeth the law, and the law inflicteth the punishment; if not so, the works of justice would be destroyed, and God would cease to be God.
(See also verse 13 of the same chapter.)
The judgment ultimately allows mercy to take effect without destroying justice. It is so much more than merely an event by which we gain salvation or are damned. It is the culmination of the Plan of Salvation, an essential truss in the bridge between justice and mercy for all of mankind. Remove the judgment and the whole Plan of Salvation would fall apart.
