It is revealing to look where the word “holy” appears in this text and what it means. The word “holiness” in both Greek and Hebrew has no particular synonym, and so it is hard to define. If you want to understand holiness, you have to look at how this word is used contextually.
In 3 Nephi, you have references to holy ones (people within the church; 5:14), to God’s holy arm (20:35), a holy city (the New Jerusalem; 20:36), holy prophets (1:13, 26; 29:2), and holy angels (27:30), along with the “Holy Ghost” (mentioned 30x in 3 Nephi). Alma 13 had also spoken dominantly, 18x, about “holy” things: holy works, God’s holy order, a holy calling, a holy ordinance, the holy order of the high priesthood, holy men, God’s holy name, holy scriptures, holy angels, holy commandments, and holy fathers. In these texts, we can identify many of these things that one would have found associated with the Holy of Holies of the biblical times. In 3 Nephi we now encounter even the holy presence of God and the very words of the Lord, as previously only the High Priest was allowed to do in the ancient Holy of Holies.
The Holy of Holies is described in Jewish literature as a place of the fullness of joy. Above all, holiness is a state of joy and rejoicing. “Joy” is mentioned, being another dominant term, 16x in 3 Nephi, especially in 3 Nephi chapters 16, 17, 27, 28. This was certainly a time of immense joy and happiness for those people. The tablets of the Ten Commandments were stored inside the Ark of the Covenant, but now Jesus preached openly new commandments in his Sermon at the Temple. The rod of Aaron, also inside the Ark of the Covenant, represented his holy Aaronic priesthood authority, and Jesus now gave the higher priesthood authority to his disciples at the end of 3 Nephi 18. The shewbread of the Temple, which could only be eaten by the one High Priest, anticipated Jesus’ miraculous administration of the sacrament, now given to all the covenant people.
Being “holy” refers to and defines all that we are striving to be as Latter-day Saints. The word “saint” (from sanctos in Latin) means “sanctified.” It means one who has been made holy. We are striving to be true and faithful Latter-day Saints, or holy ones. Holiness should define our relationships with God, our relationships within our families, our conduct within church circles, and our dealings with all other people. Everyone who has been to the temple is an anointed one and are all anointed beings, to become holy people, made holy by the Anointed One, in every way possible.
Book of Mormon Central, “What Makes 3 Nephi the Holy of Holies of the Book of Mormon? (3 Nephi 14:13–14),” KnoWhy 206 (October 11, 2016).
John W. Welch, “Seeing Third Nephi as the Holy of Holies of the Book of Mormon,” Journal of the Book of Mormon and Other Restoration Scripture 19, no. 1 (2010): 36–55; also published in Third Nephi: An Incomparable Scripture, ed. Andrew C. Skinner and Gaye Strathearn (Salt Lake City and Provo, UT: Deseret Book and Neal A. Maxwell Institute for Religious Scholarship, 2012), 1–33.