[T]he first and clearest answer has to be that the Trinity isn’t ultimately for anything, any more than God is for the purpose of anything. Just as you wouldn’t ask what purpose God serves or what function he fulfills, it makes no sense to ask what the point of the Trinity is or what purpose the Trinity serves. The Trinity isn’t for anything beyond itself, because the Trinity is God. God is God in this way: God’s way of being God is to be Father, Son, and Holy Spirit simultaneously from all eternity, perfectly complete in a triune fellowhip of love. If we don’t take this as our starting point, everything we say about the practical relevance of the Trinity could lead us to one colossal misunderstanding: thinking of God the Trinity as as a means to some other end, as if God were the Trinity in order to make himself useful. But God the Trinity is the end, the goal, the telos, the omega. In himself and without any reference to a created world or the plan of salvation, God is that being who exists as the triune love of the Father for the Son in the unity of the Spirit. The boundless life that God lives in himself, at home, within the happy land of the Trinity above all worlds, is perfect. It is complete, inexhaustibly full, and infinitely blessed.
—Fred Sanders in The Deep Things of God: How the Trinity Changes Everything.
When it comes to the study the Trinity, or the study of God in general, we’re too quick, I think, to run straight to the practical implications and ask ourselves, “What does this doctrine mean for me? How does it affect my life? And what should I do in light of this truth about God?”
Of course, learning about God does have practical implications. But first, because God as he is in himself is “the end, the goal, the telos, the omega,” we should desire to know God for his sake. To get at what God is in himself, we can ask, “What is he like ‘without any reference to a created world or the plan of salvation’?” Priority #1 is simply gazing for a while on the answer to this question and marveling at what we see.