Substance in the ordinary sense of the word, in everyday usage, is that of which a thing consists: physical matter or material form and substance, meaning a species of matter of definite chemical composition, such as: a chalky substance.
In philosophy, "sub-stance" is the essence, the unseen reality that "stands under" or is the foundation of that of which a thing outwardly consists, the real under-lying essence of actual being which is expressed by the changeable "accidents" or visible manifestations or perceptible qualities of the thing, even of persons; hence, physical matter is not of itself the fundamental substance of existence.
Trans-substance: the Catholic doctrine of "transubstantiation"
The philosophical idea of substance is what Catholic eucharistic doctrine means in saying that the substance of the bread and wine are "transubstantiated" into the substance of the body and blood of Christ including his soul and divinity, but that the outward appearances remain. The substance is changed, the matter is not. The substance of them is no longer that of food but the substance of a Person. As food in the human body is transformed in a few hours into flesh and blood and bone, so Christ in the consecration by the priest instantly unites the "elements" of the bread and wine offered on the altar to himself as being one with his whole Person, body, blood, soul, and divinity. By analogy, just as the chemical elements of food, the carbon, calcium, protein, salt, iron, copper, sugars, fats, water and trace elements, and their molecular and atomic structures, all remain what they are even after metabolism by the body, and are no longer food but flesh and blood and bone, so the food of bread and wine offered in sacrifice to Christ on the altar have been made by Christ Jesus into the real presence of Christ himself and are one with him without any apparent change in their outward appearance.
Critics who utterly reject this doctrine as an impossible absurdity say that it utterly strains all credibility by totally violating the God-given intelligence of human reason and ordinary common sense. They say that there is no evidence of any change in the substances of the bread and wine after the consecration, that bread obviously remains bread and wine obviously remains wine, and that neither one of them looks, feels and tastes like human flesh and blood, not to mention soul, and spirit and the divine nature of divinity; but when food is transformed into flesh and blood and bone the change is most definitely obvious. They point out that even under the microscope there is no evidence of human cellular tissue in the consecrated bread and wine. Even at the subatomic level, the elements of bread and wine do not change. By no reasonable stretch of the imagination do they regard the bread and wine of the eucharist as God. They conclude that Jesus was speaking only symbolically when he said, "This is my body. This is my blood." For this reason the doctrine of transubstantiation is regarded as impossible, an unintelligent, ignorant, mindless, pagan superstition.
Catholic apologists respond that as the atoms of matter are not visible under the microscope and can be transformed in the atomic laboratory from one element to another, so by analogy the change in the substance of the bread and wine is not visible. As the body is visible, the invisible soul of the living body is not. And while the forms of bread and wine and their chemical structures are visible, the invisible Christ present in those forms, whole and entire, is not. He himself is present, in Person, as God. And as in Christ Jesus the "fulness of divinity dwells bodily", the Father in him and he in the Father, so likewise in the Eucharistic elements received as food in communion the fulness of Jesus himself, body, blood, soul and divinity is present; and those who partake of communion with him partake of the divine nature.
Orthodox theologians and apologists who believe in the Real Presence of the Lord avoid explanations of transubstantiation and accept simply as divine truth the mystery as declared by Christ at the Eucharist of his Last Supper. In Christian theology, a mystery is a truth that is above the power of the understanding of human reason but not against it, reasonable but not fully accessible in its entirety to the understanding of the finite human mind.
Confusing matter with substance
The common use of the word "substance" as a synonym for "matter" is responsible for the confusion of meaning in debates over the doctrine of transubstantiation.
The doctrine of monism holds that God is the entire substance of the universe and that the whole of the universe, all of its matter and energies taken together as one undivided whole, is God (pantheism). This is the basis of Gnosticism and the practice of Magic, and the underlying dynamic of the various forms of Cosmic Humanism and New Age beliefs. According to Christian Science all of existence is Mind, the Mind of God, and matter as such does not exist in reality—thus sickness, illness and disease are only illusions of mistaken belief which can be eliminated by knowledge of the truth. According to Hinduism all of existence is merely lila, God's play, the imaginative dreaming of Brahman the only Existent One, and because there is only one existent eternal substance of reality, death is unreal, and therefore there is ultimately no need for a savior because all is in God.