Explaining the Trinity

What's the best way to explain the Triune God? I understand it's three separate entities in one unity, but just by what I said, am I saying it wrong? I want to make sure I'm correct before explaining it.

The Bible doesn’t use the terms that we use when talking about the Trinity in exactly the same way that we do. We learn from Scripture, however, that there is a certain respect in which God is absolutely, indivisibly one (Deuteronomy 4:35, Deuteronomy 6:4, 1 Corinthians 8:4, etc.), and that this one God is a self-aware ego who can speak and say “I.” We also find that the Father, the Son, and the Holy Spirit are not the same, that each of them is also a self-aware ego that can refer to himself as “I,” and that they relate to one another in certain ways (Isaiah 61:1, Mark 1:9-11, etc.). In this respect, therefore, God is not one, but three.

Over the centuries the Church has settled on “essence” as the best term for the way in which God is one, and on “person” as the best term for the way in which God is three. That’s why we speak about three distinct persons—Father, Son, and Holy Spirit—but only one divine essence.

We should be clear, however, that in choosing one term for God’s one-ness and another for God’s three-ness, we really haven’t explained anything. Scripture’s teaching of the Trinity remains an unsolvable logical paradox.