Mormons believe in the Godhead. Mormons believe that the Godhead is comprised on Heavenly Father, his son, Jesus Christ, and the Holy Ghost. They are three distinct people with three distinct roles but are united in purpose. This single purpose makes them one because they work as one being. This is what Mormons refer to as the Godhead.
According to Mormonism, God is the father of everyone living here on earth. He is the father of our spiritual bodies. Just like us, God has a spirit of flesh and bone. Mormons believe that He has a perfect spirit and a perfect, immortal physical body. We believe that we were made in his countenance.
Mormons believe that before this life, we lived in heaven with our Heavenly Father as spirits. We were happy, living in righteousness and perfection. But we could only progress so far in this state. God knew this. Mormons believe that God has a plan for us, called the plan of salvation. This plan required us, spirits at the time, to live on earth having imperfect bodies. In this life, we are to be tested and work to learn truths and return to live with our Heavenly Father when it is all done. This period of life on earth would give us the opportunity to grow and mature more independently. Heavenly Father knew that we would make mistakes. His plan, thus, included a Savior. This Savior would come to live a perfect life on the earth, then suffer and die to pay for our sins. Because of Christ’s sacrifice, we are not expected to live perfect lives. We do the best that we possibly can as imperfect people and Jesus Christ’s atonement will make up for what we lack.
Jesus, the eldest of God’s children, was chosen as the One chosen by God to bear the sins of the world. He is the second member of the Godhead. Mormons believe that Jesus physically created the world we live in. He offered himself in suffering and death to atone for the sins of all mankind. And He was resurrected, immortal, His body and spirit joined together again forever. He too has a body of flesh and bone.
The third member of the Godhead is the Holy Ghost. He differs from God and Jesus in that he does not possess a physical body. He is a spirit. This way, he can dwell within us at all times. His job is to testify of God and Jesus, he guides us in the way we should go, and comforts us. He confirms truth to us. He will teach of Christ and He will teach of the gospel. Anyone can feel his spirit, but those who are baptized into the Mormon Church can have his constant companionship. For those who live according to gospel principles, the Holy Ghost can be felt always. When we sin or put ourselves in sinful situations, he will leave.
Together, these three make up the Godhead and are united in their purpose.