Joseph Smith - Beyond the Veil: Life in the Eternities

In the New Testament we read -

"In my Father's house are many mansions: if it were not so, I would have told you. I go to prepare a place for you.
3 And if I go and prepare a place for you, I will come again, and receive you unto myself; that where I am, there ye may be also." (New Testament John 14:2 - 3)

As one reads these verses, you would have to assume that the translation of "house" may not the proper translation. The Prophet Joseph Smith taught that -

"It should be—‘In my Father’s kingdom are many kingdoms,’ in order that ye may be heirs of God and joint-heirs with me. … There are mansions for those who obey a celestial law, and there are other mansions for those who come short of the law, every man in his own order.”

This seems to make a little bit more sense. Paul suggested different kingdoms of different glory in writing the Corinthians saying that -

"There are also celestial bodies, and bodies terrestrial: but the glory of the celestial is one, and the glory of the terrestrial is another.
41 There is one glory of the sun, and another glory of the moon, and another glory of the stars: for one star differeth from another star in glory.
42 So also is the resurrection of the dead..." (New Testament 1 Corinthians 15:40 - 42)

Paul even called these kingdoms and glories as heavens saying -

"I knew a man in Christ above fourteen years ago...such an one caught up to the third heaven." (New Testament 2 Corinthians 12:2)

In the marvelous revelation given to the Prophet and Sidney Rigdon they also saw the kingdoms that Paul saw. They wrote of the kingdom of the glory of the stars saying -

"...we saw the glory of the telestial, which glory is that of the lesser, even as the glory of the stars differs from that of the glory of the moon in the firmament.
82 These are they who received not the gospel of Christ, neither the testimony of Jesus." Doctrine and Covenants Section 76:81 - 82)

The also -

"...saw the terrestrial world, and behold and lo, these are they who are of the terrestrial, whose glory differs from that of the church of the Firstborn who have received the fulness of the Father, even as that of the moon differs from the sun in the firmament.
72 Behold, these are they who died without law;
73 And also they who are the spirits of men kept in prison, whom the Son visited, and preached the gospel unto them, that they might be judged according to men in the flesh;
74 Who received not the testimony of Jesus in the flesh, but afterwards received it.
75 These are they who are honorable men of the earth, who were blinded by the craftiness of men.
76 These are they who receive of his glory, but not of his fulness." (Doctrine and Covenants Section 76:71 - 76)

But of the greatest and most desirable importance, they saw -

"...they whose bodies are celestial, whose glory is that of the sun, even the glory of God, the highest of all, whose glory the sun of the firmament is written of as being typical." (Doctrine and Covenants Section 76:70)

These -

"...are they who received the testimony of Jesus, and believed on his name and were baptized after the manner of his burial, being buried in the water in his name, and this according to the commandment which he has given—
52 That by keeping the commandments they might be washed and cleansed from all their sins, and receive the Holy Spirit by the laying on of the hands of him who is ordained and sealed unto this power;
53 And who overcome by faith, and are sealed by the Holy Spirit of promise, which the Father sheds forth upon all those who are just and true." (Doctrine and Covenants Section 76:51 - 53)

"These are they who are just men made perfect through Jesus the mediator of the new covenant, who wrought out this perfect atonement through the shedding of his own blood." (Doctrine and Covenants Section 76:69)

"Wherefore, as it is written, they are gods, even the sons of God—
59 Wherefore, all things are theirs, whether life or death, or things present, or things to come, all are theirs and they are Christ's, and Christ is God's.
60 And they shall overcome all things." (Doctrine and Covenants Section 76:58 - 60)

Of this great revelation the Prophet explained -

“Nothing could be more pleasing to the Saints upon the order of the kingdom of the Lord, than the light which burst upon the world through the foregoing vision. Every law, every commandment, every promise, every truth, and every point touching the destiny of man, from Genesis to Revelation, where the purity of the scriptures remains unsullied by the folly of men, … witnesses the fact that that document is a transcript from the records of the eternal world. The sublimity of the ideas; the purity of the language; the scope for action; the continued duration for completion, in order that the heirs of salvation may confess the Lord and bow the knee; the rewards for faithfulness, and the punishments for sins, are so much beyond the narrow-mindedness of men, that every honest man is constrained to exclaim: ‘It came from God.’ ”