The role of the Book of Mormon is clearly stated here. It will stand side by side with the Bible to establish the record of the words of the Lamb, and the records of the twelve apostles of the Lamb.
1 Nephi 13:42
42 And the time cometh that he shall manifest himself unto all nations, both unto the Jews and also unto the Gentiles; and after he has manifested himself unto the Jews and also unto the Gentiles, then he shall manifest himself unto the Gentiles and also unto the Jews, and the last shall be first, and the first shall be last.
This verse sums up the vision of redemption. Christ stands as the central redemptive figure, and his coming and providing the true gospel is the saving grace for all men. This comes in stages, however. In the first instance his mission was to the house of Israel. They were the first. The gospel is then allowed to be preached to the Gentiles, and in this they were the last.
After the initial acceptance of the truth, both the house of Israel and the Gentiles fall from the truth, and come to a point where they are believers, but in a corrupted version of the gospel, a version which cannot save them.
Into this picture comes Christ again, with a new revelation, a restoration of those things which are lost. He does this directly through the record of his visit to the Americas which is published to the Gentiles, providing them with the keys to the lost plain and precious parts of the gospel. In this the Gentiles become the first, thus the last shall be first. The Gentiles are then the ones to bring the redemption to the remnants of the house of Israel, and in this they are the last. Thus those who once were first are now the last to receive the gospel.