What is meant by the theological term transubstantiation?

Answer 1

Transubstantiation:

In Christianity, The miraculous effect whereby through the blessing and invocation of a priest the bread and wine of the Communion meal become in a mystical sense the true body and blood of Jesus Christ, while still under the guise of bread and wine.

Answer 2

Catholic AnswerThe doctrine of transubstantiation is an explanation for what Christians have always believed about the Eucharist. It is based on the teaching of St. Thomas Aquinas who explained the difference with the substance and the accident of a thing: Water = substance; Accidents = Ice, Snow, Liquid water, Steam, Vapor. The Accidents are the things that we actually sense: we touch, see, perhaps taste, etc. The substance is what the thing actually is, in this case H20. Another case, in a matter of a few years, every single cell in your body has died and been replaced by a new cell. Are you still the same person? Yes, but the "you" that is your body is completely different.
Now, back to the water. In that example, the substance remains the same, but the accidents change, radically. During the Mass, at the moment of consecration, a miracle is worked by God, and the entire substance of the bread disappears and is replaced by the substance of Jesus Christ's Body and Blood, Soul and Divinity. In a similar manner, the entire substance of the wine is gone, and is replaced by the substance of Christ's Blood, containing his Body and Blood, Soul, and Divinity. This is the reverse of what is happening when the water changes from ice to vapor, but it is just as real. The accidents of the bread and wine remain, but the substance has changed.

This was defined, in this manner, by the Council of Trent in 1551 explaining the unchanging doctrine of the Church for the previous fifteen centuries in opposition to the protestants who sought to change the belief of the Church that had been handed down from Christ to the Apostles, to us.

Another example might be wood, you could have a tree, a floor, or a pile of ashes. Same thing, they are all "wood", but with different accidents.

But in all the things we can look at in the world, the accidents can and do change, but the substance remains the same. The Eucharist is entirely the other way around, the "accidents": looks and tastes like bread - remain the same, BUT the entire substance, what it is, changes. So even though to every sense we have, even with sophisticated instruments, everything we can see, touch, etc. it remains bread; but the entire substance of bread has, through a miracle of God, changed into the substance of Jesus Christ, His Body, and Soul, His Humanity, and Divinity, are all present where previously bread had been present.

This is a great mystery, but, hey, God is all powerful, and so far beyond us as to be incomprehensible. But He condescended to become human so that we could comprehend Him. The fact that He also condescended to appear under the appearance of bread is no less a miracle than that he came as a human being.

from The Catechism of the Catholic Church, second edition, English translation 1994

1375 It is by the conversion of the bread and wine into Christ's body and blood that Christ becomes present in this sacrament. The Church Fathers strongly affirmed the faith of the Church in the efficacy of the Word of Christ and of the action of the Holy Spirit to bring about this conversion. Thus St. John Crysostom declares:

It is not man that causes the things offered to become the Body and Blood of Christ, but he who was crucified for us, Christ himself. The priest, in the role of Christ, pronounces these words, but their power and grace are God's. This is my body, he says. The word transforms the things offered. (St. John Chyrsostom, pro. Jud. 1:5: J. P. Migne, ed., Patrologia Graeca {Paris, 1857-1866} 49, 380)

And St. Ambrose says about this conversion:

Be convinced that this is not what nature has formed, but what the blessing has consecrated. The power of blessing prevails over that of nature, because by the blessing nature itself is changed . . . Could not Christ's word, which can make from nothing what did not exist, change existing things into they were not before? It is no less a feat to give things their original nature than to change their nature. (St. Ambrose, De myst. 9, 50; 52: J. P. Migne, ed., Patrologia Latina {Paris: 1841-1855} 16, 405-407