I've been asked about the Trinity more than once and, as you can imagine, I've given more than one answer. It's always a tough concept to talk through because I am trained, for better or worse, to start from what the Bible teaches about a given subject and in this case it's not taught in scripture, it's inferred. Though it's not completely clear or articulated in scripture it cannot be ignored. for example, Jesus said "therefore go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit." What could a statement like that have meant to a first century monotheistic Jew? Because of passages like this, it makes sense that the trinity was one of the earliest Christian doctrines to be established, at least by 325 at the council of Nicaea.
Whenever I am asked about the doctrine of the trinity, I always find myself dissatisfied with whatever answer I give. Either my explanation seems to trivial, too simplistic, not "biblical" enough, or just plain unimportant. I don't know how to explain the importance of trinity. Yeah God is three persons... whatever that means... so what? What does that change?
I guess there's a good reason that trinity is hard to teach... because it's not meant to be taught but prayed. The trinity must be prayed, and thus lived, in order for us to find any level of understanding. Perhaps the trinity is more of a lens than a doctrine... it gives us a way to see and participate in God's work. We begin to see the wind of the Spirit blow through our lungs as we embrace the Son in the face of the poorest of the poor with the hope of our vindication from the Father. As we live and pray trinity we live and pray in relationship, we live out the eternal community of the trinitarian God. We see trinity and that is where we begin to believe it.