What the Word "Subsistence" Means in Trinitarian Lingo

I would say that "subsistencies" within a Trinitarian context means "divine persons." For a number of Trinitarians, subsistencies are persons and persons are subsistencies (a convertible proposition)--the denotation "person" for
subsistentia is a familiar one to those who have studied Latin theology.

In this regard, I notice that the Iconoclastic Council of 754 professes:

"They [the Nestorians] fall into the abyss of impiety, since they separate the flesh from the Godhead, ascribe to it a subsistence of its own, a personality of its own, which they depict, and thus introduce a fourth person into the Trinity."

The same council declared:

"If anyone shall not confess, according to the tradition of the Apostles and Fathers, in the Father, the Son and the Holy Ghost one godhead, nature and substance, will and operation, virtue and dominion, kingdom and power in three subsistencies, that is in their most glorious Persons, let him be anathema."

Another source (The Belgic Confession, Article 8) provides this understanding of the tripersonal deity:

Nevertheless, this [triune] distinction does not divide God into three, since Scripture teaches us that the Father, the Son, and the Holy Spirit each has a distinct subsistence distinguished by characteristics—yet in such a way that these three persons are only one God.

It is evident then that the Father is not the Son and that the Son is not the Father, and that likewise the Holy Spirit is neither the Father nor the Son.

We close with these observations from Calvin:

"But to say nothing more of words, let us now attend to the thing signified. By person, then, I mean a subsistence in the Divine essence, - a subsistence which, while related to the other two, is distinguished from them by incommunicable properties. By subsistence we wish something else to be understood than essence. For if the Word were God simply and had not some property peculiar to himself, John could not have said correctly that he had always been with God. When he adds immediately after, that the Word was God, he calls us back to the one essence. But because he could not be with God without dwelling in the Father, hence arises that subsistence, which, though connected with the essence by an indissoluble tie, being incapable of separation, yet has a special mark by which it is distinguished from it" (John Calvin, Institutes of the Christian Religion 1.13.6).