God gives to Nephi the same power he gave to his apostles during his earthly ministry:
Matthew 18:18-20
18 Verily I say unto you, Whatsoever ye shall bind on earth shall be bound in heaven: and whatsoever ye shall loose on earth shall be loosed in heaven.
19 Again I say unto you, That if two of you shall agree on earth as touching any thing that they shall ask, it shall be done for them of my Father which is in heaven.
20 For where two or three are gathered together in my name, there am I in the midst of them.
The sealing power is the same, but the requirement for at least two apostles is not present in the New World because as yet there is no such quorum in the New World. The Lord puts this power in a single person in the New World. To receive such places Nephi in not only a place of respect and responsibility, but places him among a small set of men so empowered:
“Few men in the history of this world have so proved their dependability that the Lord could entrust them with power to seal upon earth and it would be sealed in heaven. Nephi was one so entrusted. God gave him mighty power in word and deed. He foretold to an angry multitude the murder of their chief judge by the latter’s own brother. He was commissioned to smite the earth with famine and pestilence, that the people might be brought to repentance and not perish in warfare. Thousands did die of the famine, but at last the people were humbled and repented, and swept the band of wicked Gadiantons from among them till the robbers became extinct. In this righteous state they esteemed Nephi a great prophet and man of God; and Lehi, his brother, was not behind him a whit in righteousness. (Archibald F. Bennett. “Nine Generations of Spiritual Leaders.” A Book of Mormon Treasury: Selections from the Pages of the Improvement Era [Salt Lake City: Bookcraft, 1959], 108.)
In spite of this small number of men to whom such absolute power has been given, aspects of this ability to seal something on earth that will be effective in heaven is at the heart of the restored priesthood. All ordinances performed by that priesthood here on earth also have a heavenly validity. In addition to this aspect of priesthood, there is a modern usage of the concept of sealing that has a specific meaning:
“Signets and seals have been used from early antiquity to certify authority. The word “seal” appears many times in the scriptures. Jesus Christ was “sealed” by God the Father (John 6:27), and Paul reminded ancient Saints that God had anointed and sealed them (2 Cor. 1:21-22) and told others they “were sealed with that Holy Spirit of promise, which is the earnest [assurance] of our inheritance until the redemption” (Eph. 1:13-14). John spoke of the servants of God being sealed in their foreheads (Rev. 7:3). In the apocryphal Acts of Thomas (verse 131), Thomas prayed that he and his wife and daughter “May receive the seal” and “become servants of the true God.” Even today licenses, diplomas, legal documents, and the like bear seals that officially attest to their authenticity.
For Latter-day Saints, the ultimate sealing power is the priesthood power given to authorized servants of the Lord to perform certain acts on earth and have them recognized (sealed) or validated in heaven. They believe it is this authority the Lord Jesus Christ described when he said to Peter, “I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven: and whatsoever thou shalt loose on earth shall be loosed in heaven” (Matt. 16:19).
The President of the Church holds and exercises the keys of sealing on earth. When a man is ordained an apostle and set apart as a member of the Quorum of the Twelve Apostles, sealing is one of the powers bestowed upon him. Other General Authorities of the Church, the presidencies of temples, and a limited number of officiators in each temple receive this sealing power during their tenure. After one is approved by the First Presidency to receive the sealing power, the President of the Church, one of his counselors, or a member of the Twelve Apostles specifically designated by the President confers the sealing power upon him by the laying on of hands. This is the specific authority to perform the temple sealing ordinances.
This is the authority by which “all covenants, contracts, bonds, obligations, oaths, vows, performances, connections, associations, or expectations” can be “made and entered into and sealed by the Holy Spirit of promise” and receive “efficacy, virtue, or force in and after the resurrection of the dead” (D&C 132:7).
In this dispensation of the fulness of times, the sealing power was restored by Elijah, the last prophet of the Old Testament period to hold it (TPJS, pp. 339-40). He bestowed that authority on Joseph Smith and Oliver Cowdery in the Kirtland Temple on April 3, 1836 (D&C 110). As each man who has been President of the Church was ordained an apostle and became a member of the Quorum of the Twelve, he had the sealing power bestowed upon him, and thus it has been transmitted to the present (D&C 110:13-16; 128:11).” (Encyclopedia of Mormonism, 1-4 vols., edited by Daniel H. Ludlow (New York: Macmillan, 1992), 1288.)