Transubstantiation is a teaching of the Church that developed from the 10th the 13th century as a way of explaining how the bread and wine that we receive at Mass are no longer bread and wine but the real body and blood of Christ. No one uses the term “transubstantiation” before the 10th century but the belief that Christ is truly present in the Eucharist goes back to the earliest Church. Christians experienced this “real presence” but didn’t know how to explain it clearly. The bread and wine they received at Mass still looked like bread and wine, but Christians believed them to become the body and blood of Christ which brought them life and spiritual growth in a special way.
The rediscovery of the philosophy of Aristotle gave medieval Christians a language in which to explore their understanding that the bread and wine of the Eucharist were not “just” signs of Jesus presence but were the real presence indeed. They combined two Latin words, “trans” meaning “across” and “substantia” meaning substance or essence.
In Aristotle’s philosophy, things can share the same nature even when they differ in some specifics. For example, a brown wooden rocking chair and a red overstuffed sofa are both recognizable as chairs, even though they look very different from one another. What makes them both “a chair” is their substance, while the size, color, shape, texture and other things that differentiate them are called “accidents.”
The teaching of transubtantiation, as summarized by St. Thomas Aquinas, the great theologian of the 13th century, was that “the whole substance of the bread is changed into the whole substance of Christ’s body, and the whole substance of the wine into the whole substance of Christ’s blood.” The accidents–color, texture, shape, and so on–remain those of bread and wine. When you eat and drink, for example, the host does not bleed. You taste bread and wine. But the substance, the very nature of this reality is now Christ’s body and blood.
This way of describing the real presence of Christ in the Eucharist worked very well for Christians in the Middle Ages, and for many years thereafter. It doesn’t work so well for many of us today. As you indicate in your question, we don’t think like Aristotle, nor do we live in a world that lives comfortably with Aristotelian terms. What is most important for us believe, however, is that Christ is present to us in the church, and in the eucharist, in a way that gives us the spiritual food we need on our life’s pilgrimage.
The teaching of Christ’s real presence in the Eucharist is, like many Catholic teachings, fundamentally a way of encountering a mystery. It attempts to provide a hint of an understanding about what is, in human terms, truly beyond understanding. We can’t wrap our minds around a mystery, but we can experience it through the eyes of faith. It engages our hearts even more than our minds, our imagination even more than our reason.
The Constitution on the Sacred Liturgy of the Second Vatican Council(1963) spoke of Christ as present in the bread and the wine of the Eucharist, in the Word of God proclaimed at Mass, in the person of the presiding minister and in the assembly gathered in worship. The eucharistic prayers of the Mass speak of the real presence in the community of believers, “the “living body of Christ” and “the living sacrifice of praise.” Pope Paul VI wrote of Christ as present in the church in such ways as prayer, works of mercy, preaching, governance, the sacraments, and finally and most fully in the Eucharist (Mysterium Fidei, 1965).
We may never fully understand, in a Western scientific sense, HOW this takes place, but if we live as members of a Christian community we do experience THAT it takes place.