In the Mormon Church the Godhead consists of three beings God the Father, Jesus Christ, and the Holy Ghost. Because of Joseph Smith's vision they believe that these three beings are separate and distinct individuals. Although they are one in purpose, heart, and power they do not occupy the same body or space.
James E. Talmage, an LDS apostle, said: "This unity is a type of completeness; the mind of any one member of the Trinity is the mind of the others; seeing as each of them does with the eye of perfection, they see and understand alike. Under any given conditions each would act in the same way, guided by the same principles of unerring justice and equity."1
God the Father is literally the spirit Father of all human beings on earth. Before being born everyone lived in heaven with God. God is perfect, all knowing, and all-powerful. He has a body of perfected flesh and bones. Man is created in the likeness of God. Because we are God's children he cares about us. His desire is for all mankind to return to live with Him after death. "For behold this is my work and my glory – to bring to pass the immortality and eternal life of man." 2
Mormons believe that Jesus Christ is the literal Son of God both spiritually and physically. He looks like his father in stature and form, just as earthly sons often resemble their fathers. Just like God the Father Jesus Christ is perfect. He has a resurrected body of flesh and bone3.
Jesus Christ is worshipped as the Savior of mankind. In the Garden of Gethsemane He redeemed man from sin and made it possible for them to return to live with God. This gift is given to those who live a righteous life. Who serve and accept Christ as their Savior either in this life or after death. It is because of the belief that people can accept Christ after death that Mormon temples are built. Within these temples members are baptized in proxy for those who have died.
On the cross and with his resurrection Christ gave another gift to mankind – that of immortality. Every person who has ever lived upon the earth will be resurrected and live forever because Christ died for them4.
The Holy Ghost is the third member of the Godhead. Unlike God the Father and Jesus Christ he does not have a body. But is a personage of spirit. It is the Holy Ghost that testifies of Christ. He acts as a comforter, teacher, and guide.
Before Christ's death he told his apostles, "But the Comforter, which is the Holy Ghost, whom the Father will send in my name, he shall teach you all things, and bring all things to your remembrance, whatsoever I have said unto you." 5 This same being is whom the Mormons believe to be the third member of the Godhead.
After Mormons are baptized they receive the Gift of the Holy Ghost, which allows the Spirit to remain with them as long as they are living righteously.
(1) James E. Talmage. Articles of Faith, p. 37
(2) Moses 1:39
(3) Luke 24:39
(4) 1 Cor. 15:22
(5) John 14:26