You are asking in general for a metaphysical understanding of the Holy Trinity of Father, Son and Holy Spirit that is a basic teaching of traditional Christianity. There is very little biblical support; the most often cited being the final words of the Gospel of Matthew: "Go therefore and make disciples of all nations, baptizing them in the name of the Father, and of the Son and of the Holy Spirit.” (Mt. 28:19).
The early church developed the creed of the Trinity to help define the role of Jesus and explain his relationship to the more familiar God of Jewish scripture and traditional belief. He was not “another” God. He was one expression of God. And God the Father, God the Son and the Holy Spirit were not separate gods; they were three different aspects of the one God.
Metaphysically, we understand the trinity to represent the aspects of Mind, Idea and Expression that help us define and work with the totality of God. God is all that is. There is nothing but God in existence. God is the name we give to the infinite energy of creative love out of which everything flows. We find it useful to understand that spiritual Source as Divine Mind, eternally creating and expressing its energy as Divine Ideas. "The divine idea that includes all divine ideas," in Charles Fillmore's definition, is the Christ—the presence of God that is the truth of our own identity. Thus we understand that the second aspect of God is not Jesus, but the Christ—the creative power which Jesus perfectly expressed, the power that lives in us in perfect potential. So we understand that we are all a part of the “Trinity.” The Holy Spirit is the energy of God, the activity of God, in all creation. It is an energy that embraces and supports us as we work to more perfectly express our own unique Oneness with God by allowing our true Christ nature to be the source for all our choices. Sometimes that Expression of God flows directly from Divine Mind; sometimes it expresses through us as we exercise our creative power and express the Christ of God into our mortal experiences.