To “be reconciled unto [Christ] through the atonement” (v. 11) is to meet the conditions for the Atonement paying for our sins. Paul later taught the same concept:
10 For if, when we were enemies, we were reconciled to God by the death of his Son, much more, being reconciled, we shall be saved by his life.
11 And not only so, but we also joy in God through our Lord Jesus Christ, by whom we have now received the atonement. [Romans 5:10–11]
Paul also said Jesus “gave himself a ransom for all” (1 Timothy 2:6), but Jesus said the Son of man came “to minister, and to give his life a ransom for many” (Matthew 20:28). Although his infinite and eternal atonement paid for the sins of all mankind, the condition for it’s being efficacious must be met. In a revelation to Martin Harris through Joseph Smith, in 1830, the Lord said:
16 For behold, I, God, have suffered these things for all, that they might not suffer if they would repent;
17 But if they would not repent they must suffer even as I;
18 Which suffering caused myself, even God, the greatest of all, to tremble because of pain, and to bleed at every pore, and to suffer both body and spirit—and would that I might not drink the bitter cup, and shrink. [D&C 19:16–18]
To “obtain a resurrection according to the power of the resurrection which is in Christ, and be presented as the first-fruits of Christ unto God, having faith, and obtained a good hope of glory” (v. 11) is to come forth in the first resurrection and receive a good or a celestial glory (see 1 Corinthians 15:40–42; D&C 88:14–20). Those who do not meet the requirements of a celestial resurrection and glory “will not attain to a perfect knowledge of [Christ]” but will “attain to the knowledge of a resurrection, and the world to come” (Jacob 4:12). Theirs will be a terrestrial or a telestial resurrection, depending on which glory they have prepared themselves to receive.
21 And they who are not sanctified through the law which I have given unto you, even the law of Christ, must inherit another kingdom, even that of a terrestrial kingdom, or that of a telestial kingdom.
22 For he who is not able to abide the law of a celestial kingdom cannot abide a celestial glory.
23 And he who cannot abide the law of a terrestrial kingdom cannot abide a terrestrial glory.
24 And he who cannot abide the law of a telestial kingdom cannot abide a telestial glory; therefore he is not meet for a kingdom of glory. Therefore he must abide a kingdom which is not a kingdom of glory. [D&C 88:21–24]
This brief treatise of the Atonement is an extension of the great sermon given by Jacob earlier and recorded in Second Nephi chapters 9 and 10.