Praying the Trinity

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.