The Book of Mormon describes Jesus Christ visiting the American continent after his resurrection in Jerusalem, sharing his Gospel message with the people there and choosing 12 more apostles -- this time from an ancient American tribe known as the Nephites. Before he left America, Jesus granted each of his American apostles a request, and three of them asked to become changed on Earth from mortal human beings into immortal angels, so they could serve people in need until Jesus returned to Earth one day. Now these three angels (who are known as "translated beings" by members of the Church of Jesus Christ of Latter-day Saints, or "LDS") are called the Three Nephites.
Here's the story of how the Three Nephites came to be famous Mormon angels who roam the Earth helping people:
The Book of Mormon records the story in 3 Nephi, chapter 28. Jesus asks his 12 Nephite apostles what they each desire after he departs, and the first nine answer: "We desire that after we have lived unto the age of man, that our ministry, wherein thou hast called us, may have an end, that we may speedily come unto thee in thy kingdom" (verse 2).
Jesus then replies to them: "Blessed are ye because ye desired this thing of me; therefore, after that ye are 72 years old ye shall come unto me in my kingdom; and with me ye shall find rest."
So Jesus promises nine of the 12 Nephite apostles salvation when they die, and tells them that they'll all die at age 72.
Next, Jesus asks the three remaining apostles what they desire, and verses 5 through 9 describe what happens:
"And they sorrowed in their hearts, for they durst not speak unto him the thing which they desired.
And he said unto them: Behold, I know your thoughts, and ye have desired the thing which John, my beloved, who was with me in my ministry, before that I was lifted up by the Jews, desired of me. Therefore, more blessed are ye, for ye shall never taste of death; but ye shall live to behold all the doings of the Father unto the children of men, even until all things shall be fulfilled according to the will of the Father, when I shall come in my glory with the powers of heaven. And ye shall never endure the pains of death; but when I shall come in my glory ye shall be changed in the twinkling of an eye from mortality to immortality; and then shall ye be blessed in the kingdom of my Father.
And again, ye shall not have pain while ye shall dwell in the flesh, neither sorrow save it be for the sins of the world; and all this will I do because of the thing which ye have desired of me, for ye have desired that ye might bring the souls of men unto me, while the world shall stand."
Here Jesus reads the thoughts of the other three apostles and decides to grant their request to stay on Earth to help save people's souls until he returns at the end of the world.
Seeing and Hearing Unspeakable Things
Next, the Book of Mormon describes Jesus departing and the three Nephite apostles getting an incredible trip to heaven, where they report witnessing incredible things while being transformed into angels, but are forbidden from discussing those things upon their return to Earth.
Verses 13 through 15 say: "And behold, the heavens were opened, and they were caught up into heaven, and saw and heard unspeakable things. And it was forbidden them that they should utter; neither was it given unto them power that they could utter the things which they saw and heard; And whether they were in the body or out of the body, they could not tell; for it did seem unto them like a transfiguration of them, that they were changed from this body of flesh into an immortal state, that they could behold the things of God."
Ministering on Earth
After the three Nephites return to Earth, verse 18 records that "...they did go forth upon the face of the land, and did minister unto all the people, uniting as many to the church as would believe in their preaching; baptizing them, and as many as were baptized did receive the Holy Ghost."
Then the Book of Mormon records a series of trials that the three Nephites suffered through but overcame: going to prison and being cast into pits, a furnace, and a den of wild animals (verses 19 through 22).
Verse 23 continues the story by describing how the three Nephites preached Jesus' Gospel message to all the ancient Nephi "...and they were converted unto the Lord, and were united unto the church of Christ, and thus the people of that generation were blessed, according to the word of Jesus."
Appearing, but Without Names
Then the prophet Mormon, whom LDS church members believe wrote the Book of Mormon, mentions that the three Nephites won't reveal their names, but they will show themselves to anyone to whom it seems good to them to appear.
Verses 25 through 30 say: "Behold, I was about to write the names of those who were never to taste of death, but the Lord forbade; therefore I write them not, for they are hid from the world. But behold, I have seen them, and they have ministered unto me.
And behold they will be among the Gentiles, and the Gentiles shall know them not. They will also be among the Jews, and the Jews shall know them not.
And it shall come to pass, when the Lord seeth fit in his wisdom that they shall minister unto all the scattered tribes of Israel, and unto all nations, kindreds, tongues and people, and shall bring out of them unto Jesus many souls, that their desire may be fulfilled, and also because of the convincing power of God which is in them.
And they are as the angels of God, and if they shall pray unto the Father in the name of Jesus they can show themselves unto whatsoever man it seemeth them good.
Power Over Temptation
The story concludes by describing how, as angels, the three Nephites have the power to overcome any temptation until judgment day comes.
Verses 38 through 40 say: "Therefore, that they might not taste of death there was a change wrought upon their bodies, that they might not suffer pain nor sorrow save it were for the sins of the world. Now this change was not equal to that which shall take place at the last day; but there was a change wrought upon them, insomuch that Satan could have no power over them, that he could not tempt them; and they were sanctified in the flesh, that they were holy, and that the powers of the earth could not hold them.
And in this state they were to remain until the judgment day of Christ; and at that day they were to receive a greater change, and to be received into the kingdom of the Father to go no more out, but to dwell with God eternally in the heavens.