Here's how the Book of Mormon (the musical) explains it:
You all know the Bible is made of testaments old an new.
You've been told it's just those two parts,
or only one if you're a Jew.
But what if I were to tell you,
there's a fresh third part out there,
Which was found by a hip new prophet
who had a little Donny Osmond flair.
You've got to believe in the first two books or you will perish without covenanting with God.
Except ye shall keep the commandments of God ye shall all likewise perish. 2 Nephi 30:1The Jews believe in the first but not the second, so god will cast them off.
As many of the Jews as will not repent shall be cast off; for the Lord covenanteth with none save it be with them that repent and believe in his Son. 2 Nephi 30:2But believing in the first two is not enough; you also need to believe in the third book, as Nephi prophesied somewhat more about.
And now, I would prophesy somewhat more concerning the Jews and the Gentiles. For after the book of which I have spoken. 2 Nephi 30:3Believing in these three books will not only get you saved, they will also turn your skin white (if God has cursed you with with dark skin) or make you delightsome (if you have become loathsome, filthy, idle, and abominable by dwindling in unbelief).
And the gospel of Jesus Christ shall be declared among them ... and their scales of darkness shall begin to fall from their eyes; and many generations shall not pass away among them, save they shall be a pure and delightsome people. 2 Nephi 30:5-6
(Note: The Mormon Church changed the word "white" to "pure" to soften the obvious racism of this prophecy.)Belief in these three books will whiten the skin of the Lamanites (Native Americans) and make the Jews a delightsome people.
And it shall come to pass that the Jews which are scattered also shall begin to believe in Christ; and they shall begin to gather in upon the face of the land; and as many as shall believe in Christ shall also become a delightsome people. 2 Nephi 30:7And it will work for you too, no matter how loathsome, filthy, idle, or abominable you are, or how dark your skin may be. You can become white and delightsome in God's eyes.
All you've got to do is believe.