D&C 85

Malachi prophesied concerning the faithful -

"...they that feared the Lord spake often one to another, and the Lord hearkened and heard; and a book of remembrance was written before him for them that feared the Lord, and that thought upon his name.
17 And they shall be mine, saith the Lord of Hosts, in that day when I make up my jewels; and I will spare them as a man spareth his own son that serveth him."  (Book of Mormon | 3 Nephi 24:16 - 17)

It appears that those who would live a celestial law would inherit celestial glory and an inheritance in His kingdom.  These that lived in this manner would be those that whose name were written in a book of remembrance.  Obviously, those that would not would not be entered thereing.

As many of the saints were striving to live a celestial law or law of consecration, there were some that would not.  Therefore, being guided by the Holy Ghost, the Prophet Joseph Smith wrote -

"It is contrary to the will and commandment of God that those who receive not their inheritance by consecration, agreeable to his law, which he has given, that he may tithe his people, to prepare them against the day of vengeance and burning, should have their names enrolled with the people of God."  (Doctrine and Covenants | Section 85:3)

In other words, those who would not covenant to live a celestial law should not have their names recorded in a book of remembrance of those that would.    Therefore -

"Neither is their genealogy to be kept, or to be had where it may be found on any of the records or history of the church.
5 Their names shall not be found, neither the names of the fathers, nor the names of the children written in the book of the law of God, saith the Lord of Hosts."  (Doctrine and Covenants | Section 85:4 - 5)

This means to me that those that would not enter into the covenant of the law of consecration, would not have there names entered and would not claim on an inheritance, whether in this life or the next for -

"...all they who are not found written in the book of remembrance shall find none inheritance in that day, but they shall be cut asunder, and their portion shall be appointed them among unbelievers, where are wailing and gnashing of teeth."  (Doctrine and Covenants | Section 85:9)

This doctrine is not new for -

"...it shall be done unto them as unto the children of the priest, as will be found recorded in the second chapter and sixty-first and second verses of Ezra."  (Doctrine and Covenants | Section 85:12)

Which reads that -

"...the children of the priests: the children of Habaiah, the children of Koz, the children of Barzillai; which took a wife of the daughters of Barzillai the Gileadite, and was called after their name:
62 These sought their register among those that were reckoned by genealogy, but they were not found: therefore were they, as polluted, put from the priesthood."  (Old Testament | Ezra 2:61 - 62)

The reason... -

"For he who is not able to abide the law of a celestial kingdom cannot abide a celestial glory."  (Doctrine and Covenants | Section 88:22)