The distinction between act and potency/ form and matter was first developed to explain natures as generated or mobile or evolving, but when Medieval Christians got a hold of it they tried to use it to answer two questions that they were very interested in: (a) How do things exist dependently on a creator? and (b) how are things individuals of some common nature (e.g. how are intelligent beings – whether human or divine – persons?) The relation that these have to catechetical instruction is obvious, with (a) being the opening chapter of any catechism on creation and (b) being the follow up chapters on the Trinity and Incarnation.
One response to (a) is that esse actualizes the union of form and matter that together constitute essentia. But how can this account preserve the distinction between finite and infinite esse? Creation can’t take part in infinite esse as infinite, and created things can’t participate in the infinite so far as the infinite is finite. This is an auxiliary reason why STA says that esse is neither infinite or finite (In octo libros Physicorum VIII l. 21) which fits into the larger context of his doctrine that esse can never be a conceptual quidditas since existence is unique and peculiar to whatever has it. Mine is not yours is not God’s. I’ve expressed this same thought by saying that esse is the unreachable limit at both ends of the Porpyrian tree: it can be approached but never reached by ascending in abstraction (since it is not a highest genus) and approached but never reached by descent to the particular (since no species divides by differences into it’s indefinite # of particulars).
The reality of existence at the downward unreachable limit to particularization is why I accept the modern Thomist idea that esse is the principle of what we call individuation while “matter signed by quantity” is simply the principle of enumeration or being countable (pace Reichmann, who swims against the tide). Aristotle’s discussion of individuation only sought to explain what we call multiplication and not the positive perfection of existing in a particular nature or of being a self, which is exactly what we are targeting in (b). This is also the reason why the Trinity shows up as the ultimate perfection of esse as such: if esse is both the upward and the downward limit of our conceptualization, then one and the same esse can exist both as a universal said of many and as its ultimate concrete particulars. In fact, we might even go further: if the act of existence and essence are the same in God, then what is intelligible about God (essence/logos/concept) is the same as both the concrete reality of God and that which embraces the Logos/ concept/ essence and the concrete reality of God. Father embraces both Logos and concrete, though as an existent containing both in a way that cannot be contained by a higher; The Son is the logos containing all that is intelligible about God – which includes and does not abstract from God’s existence; and the Holy Spirit is contained by Father and Son while being also the concrete reality of God, beyond which no further reality is possible.