Only the Catholic Church has continuously proclaimed the undeniable fact of Jesus' complete presence (body and blood, soul and divinity) in the Holy Eucharist.  As Protestant sects formed during the Reformation, opinions began to interfere with the unchangeable and uncontested dogma as taught from the beginning.  Below are the various wrinkles that have emerged as Protestant sects have put their own spin on the words of John 6...

Lutheranism -- Teaches that Christ is present, but so is the bread and wine, aka "consubstantiation". 

Anglicanism -- Believes in the "Real Presence" but only to the recipient, and not in the species of bread and wine.

Calvinism -- Teaches that a "pneumatic presence" exists in the bread and wine.  Believers receive not the flesh and blood of Christ, but are essentially making a "spiritual communion" instead. 

Methodism -- Much like Lutheranism and Calvinism, believers accept the "Real Presence" of Christ at the Eucharist, but not in any way replacing the bread and wine (grape juice). 

Transubstantiation takes place at two points of the Eucharistic prayer:  

1.  The bread becomes the Body of Christ when the priest says, "Take this all of you and eat of it, for this is my body which is given up for you."

2.  The wine becomes the Precious Blood of Christ when the priest says, "Take this all of you and drink from it, for this is the chalice of my Blood;  the Blood of the new and eternal convent, which will be poured out for you and for many for the forgiveness of sins.  Do this in memory of me."

"What you see is the bread and the chalice; that is what your own eyes report. But what your faith obliges you to accept is that the bread is the body of Christ and the chalice is the blood of Christ. This has been said very briefly, which may perhaps be sufficient for faith; yet faith does not desire instruction."

St. Augustine

1376 The Council of Trent summarizes the Catholic faith by declaring: "Because Christ our Redeemer said that it was truly his body that he was offering under the species of bread, it has always been the conviction of the Church of God, and this holy Council now declares again, that by the consecration of the bread and wine there takes place a change of the whole substance of the bread into the substance of the body of Christ our Lord and of the whole substance of the wine into the substance of his blood. This change the holy Catholic Church has fittingly and properly called transubstantiation."

1413 By the consecration the transubstantiation of the bread and wine into the Body and Blood of Christ is brought about. Under the consecrated species of bread and wine Christ himself, living and glorious, is present in a true, real, and substantial manner: his Body and his Blood, with his soul and his divinity (cf. Council of Trent: DS 1640; 1651).

"Transubstantiation" is one of them high-fallutin' words (like "consubstantial"), but "high falutin'" shouldn't be confused with "unnecessary".   For centuries, the Church has defended the perennial teaching of the Eucharist against every comer from every corner of the world.  In short, She's been in the ring since Day One, and nothing will change that.  But for the sake of describing something supernatural -- something so remarkable it can't adequately be reflected in the human language, we must resort to terminology that has great precision -- even if it doesn't completely explain the mystery.   

The Holy Spirit, in all His Wisdom, did not want something as important as the Holy Eucharist to be subject to us flailing about in search of an explanation.  Of course, Jesus said as much when He told the disciples in John 6, "The words I have spoken to you are spirit and life."  In other words, "these things are beyond your material knowledge and always will be."  Nevertheless, Our Lord gives as much transparency as we can seek, and throughout the centuries.  Although Church Fathers such as St. Justin Martyr and Ignatius of Antioch were freely affirming that the Eucharist is truly the flesh of Christ, but the idea that a "change" was taking place in the bread and wine itself was yet undiscerned.  
It was Saint Cyril of Jerusalem, in the fourth century A.D., who said: 
 

To be "surely sanctified and changed" implies a "transformation" of some kind -- not just an appearance "next to" or "about" the bread and wine.  Saint Augustine would say in the 5th century, 
 

The faithful know what I'm talking about; they know Christ in the breaking of bread. It isn't every loaf of bread, you see, but the one receiving Christ's blessing, that becomes the body of Christ.

But what was this "becoming"?  Centuries would continue to pass as the great thinkers in the Church prayed and sought out clarity.  It wasn't until the 12th century that the Archbishop of Tours, Hildebert La Vardin first used the term "transubstantiation".  Shortly thereafter, in 1215 A.D. the Fourth Lateran Council was called, and the term "transubstantiation" was introduced to the magisterial documents.

Since entry into Heaven doesn't require taking a technical aptitude test, the Church asks the faithful to ascribe to the following infallible teaching, in a spirit of Faith:
 

• The Body and Blood, Soul and Divinty of Christ are truly present in the Holy Eucharist.
• The accidents, i.e. the look, taste, feel of bread and wine, remain, but the substance is no longer wheat and fermented grapes, but the actual flesh and blood of Christ. 
• The bread and wine are no longer present; in other words, once transubstnatiation takes place, it is no longer licit to refer to the Precious Blood and the Host as "bread and wine".  
• The Lord is present in the Eucharist until such time as the digestive process breaks down the Host and/or the wine is metabolized.  

"To whom shall we go?  You have the words of Eternal Life."