Ok, here's how I understand the Trinity, please do correct me if I am wrong since I am a stupid man and my mind cannot fully comprehend the full nature of God.
What am I? I am by species a male and by genus a human who is in their 20's, and although English lacks a concrete word for an individual humans/persons ontological reality, this is what can best be said using the English language about what I am.
Who am I? I am [inserts name], I like theology and history, and from time to time I like to talk about philosophy. I am the son of a mother and father. I am the uncle of a niece and nephew. I am the brother of three sisters and two brothers. This is who I am.
Now, what is the supreme being? He is God. He is omnipresent, omnipotent, omniscient. He is simple, not composed of any parts. He is pure spirit. He is outside of time and space. He is beyond all things. God is existence within itself, and God belongs to not genus except himself. God is our English word for the ontological reality of this being.
Who is God? God is Father, Son, and Holy Spirit. Three persons, yet the one supreme being. They are completely distinct modes of existence from each other, yet they are God. They are all equal. They are all omniscient, omnipresent, and omnipotent, all having one divine will, one divine mind, and all love perfectly.
God is not divided though. The Father, Son, and Holy Spirit are not 1/3 of God. They are all fully 100% God. The Trinity in itself is the unity within God.
The Father is the source of the Trinity. He is the sole principle and originator of the Trinity. The Father sufficiently could exist as he is on his own without either the Son or Holy Spirit; though without the Son he would lack a a relational designation within his own person. The Son is eternally generated by the Father, finding his sole source in the Father. The Father gives his being to the Son, and without the Father, there could be no Son. The Holy Spirit is a single spiration of the Father through the Son, finding a double procession by going through the Son because the Father has given the Son all things except Fatherhood. Likewise, the Father has given the Holy Spirit all things except Fatherhood and Sonship (and thus nothing goes through the Holy Spirit). The Father could exist simply with the Son, or simply with the Holy Spirit, or neither at all, yet neither the Son or Holy Spirit could exist without the Father.
The Son properly is theologically Wisdom herself, or in more precise philosophical terms, the Son is the Word, the λόγος (Logos). The Word is the mind or thought of God in which God emanates out from himself as a separate mode of existence, or in more precise terms, as a separate hypostasis/person, and God gives the Word his essential nature making the Word God himself for the Word shares the same nature as the Father.
The Holy Spirit is a passive spiration of the Father, another emanation of God in which God emanates out of himself as a separate hypostasis/person, and to which he gives his essential nature to thus making the Holy Spirit God because he shares the same nature as the Father and the Son. It is my understanding that Aquinas views the Holy Spirit as the emanation of the perfect love between the Father and Son, though this isn't dogmatically defined.
(to be continued…)