What does the term, “their worm dieth not” (D&C 76:44) mean? What sources do you know that discuss this?
The verse that you refer to in the Mormon scripture, The Doctrine and Covenants, is part of the passage reprinted below:
Wherefore, he saves all except them–they shall go away into everlasting punishment, which is endless punishment, which is eternal punishment, to reign with the devil and his angels in eternity, where their worm dieth not, and the fire is not quenched, which is their torment–
And the end thereof, neither the place thereof, nor their torment, no man knows;
Neither was it revealed, neither is, neither will be revealed unto man, except to them who are made partakers thereof;
Nevertheless, I, the Lord, show it by vision unto many, but straightway shut it up again;
Wherefore, the end, the width, the height, the depth, and the misery thereof, they understand not, neither any man except those who are ordained unto this condemnation. (D&C 76:44-48)
The condemnation referred to here is the damnation to remain in hell with the devil and his angels for eternity, without forgiveness. The damnation is reserved for the sons of perdition spoken of in verse 32 to 38 of the same section, which reads as follows:
They are they who are the sons of perdition, of whom I say that it had been better for them never to have been born;
For they are vessels of wrath, doomed to suffer the wrath of God, with the devil and his angels in eternity;
Concerning whom I have said there is no forgiveness in this world nor in the world to come–
Having denied the Holy Spirit after having received it, and having denied the Only Begotten Son of the Father, having crucified him unto themselves and put him to an open shame.
These are they who shall go away into the lake of fire and brimstone, with the devil and his angels–
And the only ones on whom the second death shall have any power;
Yea, verily, the only ones who shall not be redeemed in the due time of the Lord, after the sufferings of his wrath. (D&C 76:32-38)
In verse 44, the phrase where their worm dieth not, and the fire is not quenched is an allegorical expression referring to the conditions that the damned will encounter during their endless punishment– the worm allegorical of the sufferings of the body from internal torment, and the fire being allegorical of the sufferings for the body a hostile environment..
Joseph Fielding Smith and Joseph F. Smith speak of the condition where “their worm dieth not” in the following two quotations:
“Salvation will come to the great body of humanity. The redemption of the soul is the resurrection. Salvation is to find a place somewhere in that redeemed state, freed from the realms “where their worm dieth not, and the fire is not quenched” in its fulness, or in other words redemption from that spiritual death which shall be pronounced upon the wicked when the Lord says unto them, “Depart,” and they go into the realms of Satan.” (Joseph Fielding Smith, Doctrines of Salvation, 3 vols., edited by Bruce R. McConkie, 2:, p)
“The sons of perdition, men who once were in possession of the light and truth, but who turned away from them and denied the Lord, putting him to an open shame, as did the Jews when they crucified him and said, “His blood be on us, and on our children;” men who consent, against light and knowledge, to the shedding of innocent blood, it will be said unto them, “Depart from me, ye cursed.” (Matt. 25:41) I never knew you; depart into the second death, even banishment from the presence of God for ever and ever, where the worm dieth not and the fire is not quenched, from whence there is no redemption, neither in time nor in eternity. Herein is the difference between the second and the first death wherein man became spiritually dead; for from the first death he may be redeemed by the blood of Christ, through obedience to the laws and ordinances of the gospel, but from the second, there is no redemption at all.”(Joseph F. Smith, Gospel Doctrine: Selections from the Sermons and Writings of Joseph F. Smith, compiled by John A. Widtsoe, p)