The Roman Catholic doctrine that the bread and wine, used in the Lord's Supper or Eucharist, actually become the literal body and blood of Christ at the "consecration" by the ordained priest. This is based on a super-literal reading of Christ's words, "This is my body, which is broken for you" (1 Corinthians 11:24, KJV); and on His Johannine discourse, "Except ye eat the flesh of the Son of man, and drink his blood, ye have no life in you" (John 6:53, KJV).
Roman Catholics believe that "by the words, Do this in commemoration of me (Luke 22:19; 1 Corinthians 11:24), Christ made the apostles priests. Moreover, He decreed that they and other priests should offer His Body and Blood." 
This doctrine should not be confused with the Lutheran doctrine of Consubstantiation.
- James White on Transubstantiation (YouTube)
- The Real Presence of Christ in the Eucharist, from the Catholic Encyclopedia
- The Catholic Nature of Calvin's View of the Real Presence, from Reformed Catholicism
- Calvin and the Objectivity of the Real Presence, from Reformed Catholicism