The word “substance” refers to any individual being, anything that exists in and of itself.
“Accidents” are always distinct from substance, and the substance is their source of being.
In the Eucharist: the substance of the bread and wine changes, but the accidents remain the same. That is, what they
are is now different, but what they are
like is not. The substance (very essence and being) of the bread and wine, by transubstantiation, are changed into the substance (very essence and being) of the body, blood, soul, and divinity of Jesus. Christ said “This is My body,” which would not be true if the substance of the bread were to remain there. Therefore, the substance of the bread must be completely nonexistent, but Christ’s body is completely existent in the Eucharist after consecration. So the substance of the bread and wine is changed into the substance of Christ’s body, blood, soul, and divinity. So the accidents of the bread and wine remain the same, while the substance is completely changed by divine power.
I see it as this: the miracle of the Eucharist is not comprehensible in its entirety; we can’t understand exactly everything that happens. As curious creatures with a love for God, we try to explain it to the best of our ability in human terms. Aquinas tries to
explain the miracle within Aristotle’s terminology and philosophy. By rational human thought, we can deduct that this reasoning can be held as compatible with the miracle of the Eucharist. That is, the theory does not go against any principles of what we know about the Eucharist, and can help us to understand what little we can, to the best of our ability. Aquinas is not saying that this principle completely explains the Eucharist in every possible way, but that it can be deducted that these reasonings may lead us to better glimpse, by using our best knowledge of philosophy, of some of the truths about the nature of the Eucharist.
Also:
But a rock, a car, a bird and a fish, are all made from the same components. The Greeks didn’t think so and Aquinas didn’t think so. This is perfectly understandable given their knowledge about nature. But today we know that there is no difference between what components these examples are made from. So, how do they differ in substance ?
We don’t say that a rock, car, bird, or fish are different in substance. And we don’t just say that the bread and wine turn into human flesh and blood. If we did, then I could understand your confusion. But we say that the blood and wine turn into the body, blood,
soul and divinity of Christ. Now we believe that God, an uncreated being, who is in nature Spirit, differs in “substance” than any created being made of matter. (Now humans have spirits as well but this is besides the point, as we are taking about matter (bread/wine) turning into a different substance (body and blood, joined with the spirit/divinity of God.) In this way, the essence and being of God’s divinity, fully present in the incarnate Christ, differs than bread or wine (created non-living matter.)