Trinity sunday is one of the few Sundays I enjoy discussing theology. The doctrine is a bit confusing as it seems esoteric and obscure.
Aside from atheism, the Trinity is the best theological response to human suffering. By and large, when people suffer, they perceive an antagonistic relationship with nature and other people. The trinity reaffirms, however, how cooperation is the center of human and divine life. Within the trinity, the aspects of God we perceive (God through nature in the Father; God through other persons in the Son; God through events via the Holy Spirit), are not divinely competitive. Their relationship is understood as mutually enforcing.
God thus understands empathy through the suffering voice of Jesus, in whom the face of victimization is revealed. Through Jesus' humanity, his eyes become our eyes through the spirit, which is the moment of revelation where we imitate each other through affectation and cooperation.
In this way cooperation - honest, difficult and forgiving cooperation - is at the center of the Christian life. We are not reduced to being nice persons: we are expected to keep our integrity, maintaining some distance (thus the independent nature of each of the persons), but we still work together as best as we are able.
The notion of transcendence and omnipotence is corrected by a realistic understanding of the brokenness of God, nature and persons - thus the trinitarian division of the single nature of God. The trinity describes how a new relationship based on cooperation - especially between the competitors of fathers and sons - is changed into one that is without rivalry, with persons who have integrity, by still recognizing each other's same divinity.