from Kevin DeYoung:
If any doctrine makes Christianity Christian, then surely it is the doctrine of the Trinity. The three great ecumenical creeds-- the Apostles' Creed, the Nicene Creed, and the Athanasian Creed-- are all structured around our three in one God, underlying the essential importance of Trinitarian theology. Augustine once commented about the Trinity that "in no other subject is error more dangerous, or inquiry more laborious, or the discovery of truth more profitable." More recently, Sinclair Ferguson has reflected on "the rather obvious thought that when his disciples were about to have the world collapse in on them, our Lord spent so much time in the Upper Room speaking to them about the mystery of the Trinity. If anything could underline the necessity of Trinitarianism for practical Christianity, that must surely be it!"
...why does any of this matter? There are lots of reasons, but borrowing from Robert Letham's work, and in Trinitarian fashion, let me mention just three.
One, the Trinity matters for creation. God, unlike the gods in other ancient creation stories, did not need to go outside himself to create the universe. Instead, the Word and the Spirit were like his own two hands (to use Irenaeus' famous phrase) in fashioning the cosmos. God created by speaking (the Word) as the Spirit hovered over the chaos. Creation, like regeneration, is a Trinitarian act, with God working by the agency of the Word spoken and the mysterious movement of the Holy Spirit.
Two, the Trinity matters for evangelism and cultural engagement. I've heard it said that the two main rivals to a Christian worldview at present are Islam and Postmodernism. Islam emphasizes unity-- unity of language, culture, and expression-- without allowing much variance for diversity. Postmodernism, on the other hand, emphasizes diversity-- diversity of opinion, belief, and background-- without attempting to see things in any kind of meta-unity. Christianity, with its understanding of God as three in one, allows for diversity and unity. If God exists in three distinct Persons who all share the same essence, then it is possible to hope that God's creation may exhibit stunning variety and individuality while still holding together in a genuine oneness.
Three, the Trinity matters for relationships. We worship a God who is in constant and eternal relationship with himself as Father, Son, and Holy Spirit. Community is a buzz word in American culture, but it is only in a Christian framework that communion and interpersonal community are seen as expressions of the eternal nature of God. Likewise, it is only with a Trinitarian God that love can be an eternal attribute of God. Without a plurality of persons in the Godhead, we would be forced to think that God created humans so that he might show love and know love, thereby making love a created thing (and God a needy deity). But with a biblical understanding of the Trinity we can say that God did not create in order to be loved, but rather, created out of the overflow of the perfect love that had always existed among Father, Son, and Holy Spirit who ever live in perfect and mutual relationship and delight.