Latter-day Saint scripture has long made clear that the Godhead–or the persons of God the Father, Jesus Christ, and the Holy Ghost–are three, distinct personages. Instructions given by Joseph Smith canonized as Doctrine & Covenants 130 read in part as follows:

The Father has a body of flesh and bones as tangible as man’s; the Son also; but the Holy Ghost has not a body of flesh and bones, but is a personage of Spirit. Were it not so, the Holy Ghost could not dwell in us (Doctrine & Covenants 130:22)

This understanding of the nature of God is a radical departure from other religious notions of God (see #50 HEAVENLY FATHER HAS A BODY OF FLESH AND BONES). 

Part of the beauty and wonder of this doctrine is that it places the Father, the Son, and the Holy Ghost into a different kind of relationship. While mainstream Christianity places the relationship as one of identicality and sameness, the Latter-day Saint understanding allows the Godhead to be understood as a social trinity. A social trinity is defined by the united and indwelling relationship of the three persons that constitute the trinity. A social trinity emphasizes their three-personness and their unity by virtue of their relationship with one another.¹¹²

This understanding, in turn, invites us to understand how we can enter into a similarly-loving and united relationship as the Godhead. 

Latter-day Saint understandings of God and their understanding of the scriptures that undergird those beliefs invite all men and women to come into a relationship with a God that is knowable and whose love and goodness are actually emulable. It is a gift without parallel.