The trinity of the Christian God includes a very important message: the Christian God must be good - he cannot be a strong, proud and violent ruler like a monotheistic god because he is triune.

What is the reason why the Christian God exists in three person for ever and ever?
God has to prove that he is good.
How does he do that?
The person of the Godhead which we call the Son is in a way the personified heart of God, the Father. Imagine, dear reader, your self could leave you, and become and independent person.
In normal life, people equipped with divine power would quarrel over the throne of the universe.
Not so, the persons of the Godhead.
Jesus, God, the Son, did not attack the Father in order to get the throne. Jesus which we thoroughly can call God was so humble that he did not hang on to be in the form of God but became man, and he even took the cup of sorrow out of the hand of the Father.
The wit is that the Father had done the same if he had incarnated instead of the Son.
The communion between Father and Son is the Holy Spirit.