One of my favorite theologians, Frederick Buechner, wrote in his book Wishful Thinking: "The much-maligned doctrine of the Trinity is an assertion that, appearances to the contrary notwithstanding, there is only one God.Father, Son and Holy Spirit (or Creator, Redeemer, Sustainer) mean that the mystery beyond us, the mystery among us and the mystery within us are all the same mystery." 

Thus the Trinity is a way of saying something about us and the way we experience God.The Trinity is also a way of saying something about God and the way God is within Godself, i. e., God does not need the Creation in order to have something to love because within Godself love happens.

The Trinity is all about love and relationship.  The three persons of the Trinity are in a loving relationship with each other - so much so that it is impossible to tell where one begins and another ends.  As humans, if we embrace the concept of Ubuntu, which tells us that all of humanity is inextricably interconnected, we have a model in the Trinity for our own relationships.  But instead of God in three persons, we have humanity in 7 billion persons!   In both of these cases, the whole is formed through diverse, though not distinct, components; in each case, there is unity in diversity.