3 Nephi 12: 5:
"And blessed are the meek, for they shall inherit the earth."
This earth abides by a Celestial Law. (D&C 88: 25.) Therefore, it is destined to become a Celestial Kingdom because it will be sanctified by a Celestial Law. (D&C 88: 25-29.) The destiny of the earth is glory. (D&C 84: 101.) Therefore, to "inherit the earth" is to inherit a Celestial Glory.
Since this is so, you need to understand the definition of "meekness." Elder Hales made these remarks about "meekness" in General Conference: "To be meek, as defined in Webster’s dictionary, is 'manifesting patience and longsuffering: enduring injury without resentment.' Meekness is not weakness. It is a badge of Christian courage." (Christian Courage: The Price of Discipleship, October 2008 General Conference, Elder Robert D. Hales.)
I've given another explanation in Beloved Enos. There I explained it is necessary to be meek first before being trusted with great power. The power to seal on earth and in heaven is something which cannot be handled apart from meekness. Without meekness a man cannot be trusted with such a power. When Enos used the power, he did so meekly. He asked rather than pronounced. He petitioned rather than decreed. Though the Lord would hearken to his words, he refrained from acting.
This is because the proper way to use such authority is only and strictly in conformity with the Lord's will. The reason Nephi received the authority was because he was meek. The account of the conferral is also the account of his qualification: "Blessed art thou, Nephi, for those things which thou hast done; for I have beheld how thou hast with unwearyingness declared the word, which I have given unto thee, unto this people. And thou hast not feared them, and hast not sought thine own life, but hast sought my will, and to keep my commandments. And now, because thou hast done this with such unwearyingness, behold, I will bless thee forever; and I will make thee mighty in word and in deed, in faith and in works; yea, even that all things shall be done unto thee according to thy word, for thou shalt not ask that which is contrary to my will. Behold, thou art Nephi, and I am God. Behold, I declare it unto thee in the presence of mine angels, that ye shall have power over this people, and shall smite the earth with famine, and with pestilence, and destruction, according to the wickedness of this people. Behold, I give unto you power, that whatsoever ye shall seal on earth shall be sealed in heaven; and whatsoever ye shall loose on earth shall be loosed in heaven; and thus shall ye have power among this people. And thus, if ye shall say unto this temple it shall be rent in twain, it shall be done. And if ye shall say unto this mountain, Be thou cast down and become smooth, it shall be done. And behold, if ye shall say that God shall smite this people, it shall come to pass.And now behold, I command you, that ye shall go and declare unto this people, that thus saith the Lord God, who is the Almighty: Except ye repent ye shall be smitten, even unto destruction." (Helaman 10: 4-11.)
This is meekness. First, Nephi had conducted his life meekly. He did not fear others. He was not afraid to lose his standing, even his life. He kept God's commandments to him above all else. He possessed an iron will, his face like flint, unwilling to waiver from what the Lord would have him say and do. He could not be tempted to betray the Lord's will. Therefore, the Lord knew by the way Nephi lived his life that he would "not ask that which is contrary to [the Lord's] will." Never.
Therefore, when the Lord had tried him and determined he was willing to serve Him at all costs, he qualifies to receive trust from God. That trust allows the Lord to confer upon the man great power. (See also TPJS p. 150: "After a person has faith in Christ, repents of his sins, is baptized for the remission of his sins, and receives the Holy Ghost (by the laying on of hands), which is the first Comforter, then let him continue to humble himself before God, hungering and thirsting after righteousness and living by every word of God. The Lord will soon say unto him, 'Son, thou shalt be exalted.' When the Lord has thoroughly proved him and finds that the man is determined to serve him at all hazards, then the man will find his calling and election made sure.")
Meekness is required to qualify for great power. And you know a man is meek when, having great power, he uses it strictly in conformity with the Lord's will; never varying from the Lord's command, and never pursuing his own agenda. This kind of meekness is men is a rare thing. Nephi, after receiving that power, was instructed that he was to deliver the Lord's message: "thus saith the Lord God, who is Almighty: Except ye repent ye shall be smitten, even unto destruction." It is the Lord's judgment. It is a meek man who delivers it. But such judgments only come after the Lord has a meek soul upon whom He can place this trust. For He has covenanted to always first employ such a servant before imposing judgments upon mankind. (Amos 3: 7.)
Therefore, when the Lord teaches the "meek shall inherit the earth" it is a statement which includes exaltation for the meek. It is one of the Lord's deepest teachings, and most profound descriptions of those who will be exalted and why.