The belief that the bread and the wine used in the Mass is, at its consecration, transformed into the actual body and blood of our Lord Jesus Christ. Its total repudiation by the Reformers was one of the hallmarks of the Reformation.
Transubstantiation was first pronounced an essential part of Catholic belief by Pope Innocent III (r.1198-1216) at the Lateran Council in 1215, and further endorsed by the Council of Trent in its 13th Session in 1551.
While it is easy to dismiss the idea of transubstantiation as pure superstition, we must not forget that the Church then felt it had sound rational arguments in upholding it. That argument was given its rational foundation when Thomas Aquinas, the Common Doctor of the Catholic Church, drew upon the Aristotelian distinction between substance (i.e., the essential matter of a thing) and accidents (the outer, non-essential qualities of the thing). When the priest consecrates the bread and wine, the substance of the elements are turned into the substance of the body and blood of Christ, while their accidents remain those of bread and wine.
Though the world has moved on and no one any longer takes Aristotle's distinction seriously, it is a concept still used used in computer science. You will notice a short black line dividing this article into its separate parts. The line is, of course, an image. We all know digital images take up space in the computer memory. The light-gray line image you see on this column, e.g., takes up 47.2 KB. But this black line occurs several thousand times on this website. One would assume, therefore, several megabytes of space are needed. In fact, the space it occupies in the server memory is still only 47.2 KB. There is only one image there. All the thousands of instances of that image found on the website are mere accidents, called up by a line of code taking up less than a hundred bytes of space in the memory. I am, to be sure, not advocating we return to transtanstiation; just trying to caution easy and superficial dismissal of views we disagree with.
The Roman Catholic Church has for some time now lightened its endorcement of transubstantiation, and esp., since Vatican II. Jesuit scholar, A. M. Bermejo, notes how "Vatican II, in more than a hundred eucharistic references spread throughout its sixteen documents, does not use the tridentine expression even once. Pope Paul [VI, r.1963-78], however, still retains the term in . . , but theologians [presumably Roman Catholic] continue to show a justifable reluctance to use the controversial word" ("Growing Convergence on the Eucharist," Indian Journal of Theology 21.4 (1972):206, n23).
Further Reading & Resources:
"Does the Doctrine of Transubstantiation Involve a Material Change?" Churchman 42.3 (1928):213-7.
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