Trinity: Ineffable Mystery

First, the systematic theology way.

Frank Sheed, Theology and Sanity, on the Trinity on this, the feast of the Holy Trinity:

The First Person knows Himself; His act of knowing Himself produces an Idea, a Word; and this Idea, this Word, the perfect Image of Himself, is the Second Person.

The First Person and the Second combine in an act of love and ... produce a state of Lovingness within the Divine nature. Into this Lovingness, Father and Son pour all that they have and all that they are, with no diminution, nothing held back.

Thus their Lovingness too is Infinite, Eternal, Living, Someone, A Person, God.

Thus the Son is generated by way of knowledge and the Spirit is breathed, or spirated, by way of Love.

Now the Theology of the Body way:

Can you see now how the very image of the Godhead is imprinted on human nature? A man and a woman when they have intimate knowledge of each other, when they give themselves to each other completely with nothing held back, then a third person, a child, comes into being by way of Love.

[This ineffable mystery can barely be comprehended by our poor finite brains.]