Father is the source, origin, essence, root, creator of all. Son is that which proceeds from, is begotten of the Father, like Him in nature, and essentially all that the Father is. Holy Spirit is God's word in movement: the working, moving, breathing, brooding of Spirit, made known to men through revelation, inspiration, and guidance. The Holy Spirit is the Comforter who will bring all things to their remembrance.
The doctrine of the trinity is often a stumbling block, because we find it difficult to understand how three persons can be one. Three persons cannot be one, and theology will always be a mystery until theologians become metaphysicians.
God is the name of the all-encompassing Mind. Christ is the name of the all-loving Mind. Holy Spirit is the all-active manifestation. These three are one fundamental Mind in its three creative aspects.