We have said this before: The Trinity is a tricky idea to grasp.
Sometimes folks talk about different persons of the Trinity...sometimes folks describe the Trinity as different manifestations of God...sometimes people delve in to metaphors (three points of the same leaf, three folds in a napkin)...the difficulty is that all of these, while partially illuminating, all fall short.
The term The Trinity was created by Christians. Jesus doesn't talk about it, Paul doesn't use the term, it is not found in your bible or mine. As far as we know it was first used (at least written) by a guy named Theophilus of Antioch in 180 BCE. As the Christian faith grew and matured and folks were trying to get a handle on these three ways of experiencing God and express them in credal statements others could agree on, the term was born.
And so, what do we do with it?
How is the Trinity important to us?
chapter of Genesis. Here we see God specifically reaching out and creating and caring and loving the Creation. An interesting bit in this passage creates some possibly different Trinitarian questions....in chapter 1, verse 26 God is quoted as saying, "Let US make humankind in OUR image, according to OUR likeness..." (emphasis ours). What do you make of that? Who was God speaking to or with at the beginning of Creation? Could be angels....could be Jesus...could be.....?
In Psalm 8 we see an example of how we has humans relate to God the Father. Much of the time we see God the Father as a protector and provider and the creator. An omnipotent presence in the world and our lives. Now this can become problematic for folks who have a negative experience of "father." We happen to think that there is flexibility here (although many will argue with that) - this passage is about a protector, provider, creator.
In the end of Paul's letter to the followers of Jesus in Corinth we can see some of the beginning of Trinitarian thinking. He closes his letter with, "The grace of the Lord Jesus Christ, the love of God, and the communion of the Holy Spirit be with all of you." Wouldn't it be fantastic if we ended every interaction that way?
And in Jesus' closing words as recorded in the gospel of Matthew we find Jesus offering us a phrase that is still used in many ways in churches today...."baptizing them in the name of the Father and of the Son and of the Holy Spirit....". This is new language to them. Jesus is certainly clearly laying out for his followers where his authority comes from and how it connects to God the Father, AND he connects himself to the Holy Spirit / Comforter that he had promised would be with them. We wonder how long they "chewed" on that commission.
God interacts with us in a variety of ways, and we interact with God in a variety of ways.