"Substance" here means what something is in itself. (For more on the philosophical concept, see Substance theory.) A hat's shape is not the hat itself, nor is its colour the hat, nor is its size, nor its softness to the touch, nor anything else about it perceptible to the senses. The hat itself (the "substance") has the shape, the colour, the size, the softness and the other appearances, but is distinct from them. While the appearances, which are referred to by the philosophical term accidents, are perceptible to the senses, the substance is not.
When at his Last Supper, Jesus said: "This is my body", what he held in his hands still had all the appearances of bread: these "accidents" remained unchanged. However, the Roman Catholic Church believes that, when Jesus made that declaration, the underlying reality (the "substance") of the bread was converted to that of his body. In other words, it actually was his body, while all the appearances open to the senses or to scientific investigation were still those of bread, exactly as before. The Catholic Church holds that the same change of the substance of the bread and of the wine occurs at the consecration of the Eucharist when the words are spoken "This is my body ... this is my blood." In Orthodox confessions, the change is said to take place during the prayer of thanksgiving.
Believing that Christ is risen from the dead and is alive, the Catholic Church holds that, when the bread is changed into his body, not only his body is present, but Christ as a whole i.e. body and blood, soul and divinity. The same holds for the wine changed into his blood. This belief goes beyond the doctrine of transubstantiation, which directly concerns only the transformation of the bread and wine into the body and blood of Christ.
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The Roman Catholic Church considers the doctrine of transubstantiation, which is about what is changed, not about how the change occurs, the best defence against what it sees as the mutually opposed interpretations, on the one hand, a merely figurative understanding of the Real Presence of Christ in the Eucharist (it teaches that the change of the substance is real), and, on the other hand, an interpretation that would amount to cannibalistic eating of the flesh and corporal drinking of the blood of Christ (it teaches that the accidents that remain are real, not an illusion, and that Christ is "really, truly, and substantially present" in the Eucharist
