This doctrine holds that the elements are not only spiritually transformed, but are actually (substantially) transformed into the Body and Blood of Christ. The elements retain the appearance or "accidents" of bread and wine, but are indeed the actual Body and Blood of Christ, the true, real, and substantial presence of Jesus in the Eucharist. For this reason, what remains of the sacrament after the Communion procession is reserved in the Tabernacle, where it can be used for later Masses, for private devotion and prayer, as well as for public Eucharistic adoration
Catholicism
The Catholic Church holds that Christ directly instructed the Apostles in belief in the real presence, that the elements of the Eucharist become the body and blood of Christ. The Synoptic Gospels present the words of Christ concerning the bread and wine at the Last Supper: "This is my body... This is my blood" (Matthew 26:26-28).
The Gospel of John records that Jesus said: "Unless you eat the flesh of the Son of Man and drink his blood you have no life in you" (John 6:53). Many of those who heard Jesus's words appear to have taken them literally, as the majority were shocked and left him. Adherents to Jewish Law consider eating blood one of the worst transgressions of kashruth, the law of eating and drinking, and a violation of the noachide laws which apply to all people and not just Jews.
St. Paul implies an identity between the apparent bread and wine and the body and blood of Christ when he writes: "Whoever, therefore, eats the bread or drinks the cup of the Lord in an unworthy manner will be guilty of profaning the body and blood of the Lord" (1 Corinthians 11:27).
Catholic doctrine is that because Christ is Risen, His Body and Blood are reunited; therefore, not only is each Host both the Body & Blood, but each sip of Consecrated wine is also both the Body & Blood. The Council of Trent decreed that all of Christ, His Body, Blood, Soul, & Divinity are fully present in each species:
For we do not receive in the Sacred Host one part of Christ and in the Chalice the other, as though our reception of the totality depended upon our partaking of both forms; on the contrary, under the appearance of bread alone, as well as under the appearance of wine alone, we receive Christ whole and entire (cf. Council of Trent, Sess. XIII, can. iii)..
Catholics use the term Real Presence to refer to Christ's actual presence in the Eucharist. Because Catholics believe the Eucharist is really and truly Christ Himself under the appearances of bread and wine, Catholics worship and adore the Eucharist. Catholics do not believe that this worship and adoration is idolatry, as they are worshipping what they truly believe to be Christ, not a mere commemoration or representation of Him.
The Catholic Church does not view the Eucharist of the Protestant communities to be valid, as under Catholic doctrine the Protestant ministers lack the sacramental power to confect transubstantiation, even if they claim to possess it.