Joseph Smith related the following:
“And we saw a vision of the sufferings of those with whom [Satan] made war and overcame, for thus came the voice of the Lord unto us:
“Thus saith the Lord concerning all those who know my power, and have been made partakers thereof, and suffered themselves through the power of the devil to be overcome, and to deny the truth and defy my power –
“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;” (D&C 76:30-37).
The language used here was used later that year in the revelation on priesthood that became D&C 84; "no forgiveness in this world nor in the world to come." These key phrases and the patterns found in these scriptures tell you they are all talking about the same thing. Those who run the risk of losing the opportunity for salvation in this world and in the next are those who have obtained the Holy Priesthood, which is to "know [God's] power" and to be made a "partaker thereof." Those who altogether turn therefrom are the "only ones on whom the second death shall have any power."
The keys of this priesthood consist in obtaining the voice of God. He will talk with those who obtain this priesthood in a familiar and friendly manner. They will receive the keys, covenants, power, and glory which God gave to Adam in the beginning (TPJS, p. 175). They are the sons of God.
Notice, the Lord purposefully showed Joseph and Sidney the "sufferings of the ungodly" immediately preceding the vision of those "who shall come forth in the resurrection of the just" (D&C 76:50). The description given beginning in v. 51 and continuing through v. 70 is of those who become "the sons of God" (D&C 76:58). The sons of God and the sons of perdition are contrasted as opposites. The sons of perdition are "ordained unto" their condemnation, while the sons of God are ordained "kings and priests" (D&C 76:48, 56).
To behold the one, was to behold the other. To have power to obtain the one, is to have it within your capacity to succumb to the other.