Historically the Latter-day Saint (or "Mormon") understanding of personhood has taken two primary forms. Both of them have implications for how we understand the nature of God, though only one of them appears to be common today. Since non-Mormons often have trouble with the Mormon understanding of God, perhaps explaining how we understand persons will help clear up some of what we say about divinity.
One of the earliest references to the Mormon understanding of persons is found in a revelation through Joseph Smith in 1835. Over a period of several months Smith revealed a text that he said was originally written by Abraham. Part of that revelation says:
And the Lord said unto me: These two facts do exist, that there are two spirits, one being more intelligent than the other; there shall be another more intelligent than they; I am the Lord thy God, I am more intelligent than they all." (Abraham 3:19)
In 1833, in an earlier revelation, Smith had already said, "Man was also in the beginning with God. Intelligence, or the light of truth, was not created or made, neither indeed can be" (D&C 93:29). Something about persons is uncreated. In time these verses became important proof-texts for Mormons, but they were largely ignored by the earliest church members. They were not central to early Mormon self-understanding or preaching.
It is easy to misunderstand these two revelations because in them Smith doesn't use the word "intelligence" the way we use it today. Noah Webster's 1828 dictionary, gives four meanings for the word: 1) understanding or skill; 2) notice or information; 3) "commerce of acquaintance," in other words shared understanding between people; and 4) "a spiritual being." In Mormon discourse, the last of these is the relevant one.
Given the usage we see in Webster, it is not surprising that early Mormons used the terms "intelligence" and "spirit" interchangeably and in a variety of ways in keeping with the variety of ways that "spirit" can be used. Contemporary Mormons, however, have resolved the equivocation and use the term "intelligence" theologically only to refer to the uncreated part of a person. That is how I use it here.
Based on Smith's revelations, Mormons believe that there is something uncreated about the individual person, and they call that uncreated part "intelligence." As Smith said, "The Spirit of Man is not a created being; it existed from Eternity and will exist to eternity" (Ehat and Cook, The Words of Joseph Smith 9). Though Smith established Mormon beliefs by revelation rather than by reason, he sometimes gave explanations of his revelations, and his explanation of the eternality of human intelligence was: "Anything created cannot be eternal" (ibid.).
It is not clear exactly how the doctrine of intelligence was understood during Smith's lifetime. Nevertheless, by 1845 (a year after Smith's assassination) a more systematic doctrine of intelligence began to coalesce. One evidence is the poem "My Father in Heaven," now the LDS hymn "O My Father." The poem was written by Eliza R. Snow, a plural wife of Smith. In that poem Snow says that individual spirits were begotten by heavenly parents. A later Mormon prophet, Wilford Woodruff, said that Snow's poem was a revelation (Millennial Star, 56:229, April 9, 1894), and it appears that most Mormons had already accepted it as teaching true doctrine.
On the view taught in Snow's poem, the individuation of personal existence begins at premortal spirit birth. That spirit is formed from intelligence, which is an elemental substance or material and not individuated. With interesting and sometimes outrageous variations and speculations, particularly by the apostle Orson Pratt and his brother, Parley P. Pratt, also an apostle, this was the principle understanding among Latter-day Saints from 1845 to about 1900.Few, if any, appear to have thought otherwise.
It isn't clear when the idea began to change, but in October of 1895 a professor from Brigham Young University, Nels L. Nelson, wrote an article for an LDS magazine aimed at Mormon young people. There Nelson identifies intelligence with the uncreated individual rather than with elemental substance ("Theosophy and Mormonism," The Contributor 16.12: 737-738).