See also:
Deification, Divinization, Theosis
Heavenly Father and Heavenly Mother
The Nicene Creed erased the anthropomorphic nature of God
Thomas Jefferson on the Trinity
From LDS.org: Scholars have long acknowledged that the view of God held by the earliest Christians changed dramatically over the course of centuries. Early Christian views of God were more personal, more anthropomorphic, and less abstract than those that emerged later during Christianity’s creedal stage. The key ideological shift that began in the second century, after the loss of apostolic authority, resulted from a conceptual merger of Christian doctrine with Greek philosophy.
Latter-day Saints believe the melding of early Christian theology with Greek philosophy was a grave error. Chief among the doctrines lost in this process was the nature of the Godhead. Latter-day Saints hold that God the Father is an embodied being with the attributes ascribed by the earliest Christians. That belief is consistent with the early Christian views of God, yet it differs from the later creeds.
We are all literally children of God, spiritually begotten in the premortal life. As His children, we can be assured that we have divine, eternal potential and that He will help us in our sincere efforts to reach that potential.
Heavenly Father is the Supreme Creator. Through Jesus Christ, He created heaven and earth and all things in them (see Moses 2:1). Alma said, “All things denote there is a God; yea, even the earth, and all things that are upon the face of it, yea, and its motion, yea, and also all the planets which move in their regular form do witness that there is a Supreme Creator” (Alma 30:44).
Our Father in Heaven wants us to dwell with Him eternally. His work and glory is “to bring to pass the immortality and eternal life of man” (Moses 1:39). In order to make this possible, He prepared the plan of salvation. He sent His Beloved Son, Jesus Christ, to loose the bands of death and atone for the sins of the world: “For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life” (John 3:16). This sacrifice is the greatest expression of our Father’s love for us. (LDS.org, Topics, God the Father)
A True and Living God
The God of Joseph Smith is the same God known to the ancient prophets; he is not the God of the philosophers nor is he the God of the creeds of Christendom. Joseph Smith was not a teacher of speculative theology, he was a personal witness of the God of heaven. That God who stood face-to-face with his prophets in times past stood in like manner before Joseph Smith and spoke to him as one man speaks to another. He was and is a knowable God, not a God hidden in a shroud of mystery. He is not a spirit essence but rather an exalted, resurrected, and glorified man. Indeed, Man of Holiness is his name. He is the Father of our spirits, we are his children born in heavenly realms where we once lived with him, and thus we rightfully call him our Father in Heaven. His work and glory is to bring to pass our immortality and eternal life. Ours is a divine destiny. Our spirits and our bodies were created in his image and likeness, and in the resurrection they will be inseparably united that we might experience both a fulness of joy and the fulness of all that our Eternal Father has.
Such was the testimony and doctrine of the Prophet Joseph Smith. Such is the message that we seek to echo to the ends of the earth. (Joseph Fielding McConkie, Sons and Daughters of God: The Loss and Restoration of Our Divine Inheritance, Bookcraft, 1994, p. 205)