Transubstantiation is the daily miracle of the Holy Catholic Church, whereby ordinary bread and wine become the body and blood, soul, and divinity of Jesus Christ during Holy Mass. Transubstantiation means the substance part of the bread and wine elements changes; but the accidental parts--sight, taste, smell, touch--do not. Catholics believe that since Jesus said it and He is God, he can do it. They believe! "Transubstantiation" merely labels it. This term was coined in the 1200's, but the reality of the change of substance from ordinary bread and wine into the body, blood, soul, and divinity of Jesus Christ was believed by the apostles and their successors from the day of the Last Supper to the present. So many anti-Catholics walk by sight, not by faith in regards to the Eucharist, but that is the exact same mistake the Pharisees and the Roman soldiers made about Jesus. If they could have seen him at His Transfiguration like Peter, James, and John did, they never would have treated Him with any disrespect. Similarly, if we could all see what the Eucharist REALLY is, we would all beg to be in the Blessed Sacrament Chapel 24/7 adoring Christ! But Catholics walk by faith, not by sight (2 Corinthians 5:7)! The entire congregation present at Mass becomes simultaneously present in heaven during the words:
"And so, Father, we bring you these gifts. We ask you to make them holy by the power of your Spirit, that they may become the body and blood of your Son, our Lord Jesus Christ, at whose command we celebrate this Eucharist." (The Epiklesis, or the Invocation of the Holy Spirit).
"On the night he was betrayed, he took bread and gave you thanks and praise. He broke the bread, gave it to his disciples, and said: Take this, all of you, and eat it: this is my body which will be given up for you." (The Consecration of the Bread)
"When supper was ended, he took the cup. Again he gave you thanks and praise, gave the cup to his disciples, and said: Take this, all of you, and drink from it:this is the cup of my blood, the blood of the new and everlasting covenant. It will be shed for you and for all men so that sins may be forgiven. Do this in memory of me." (The Consecration of the wine).
The altar is surrounded by the heavenly host of angels and saints, who also participate in the same responses we say at Mass - the Holy, Holy, Holy, for example, from Isaiah 6:3 and Revelation 4:8. And since we know for a fact that those in Heaven are one Spirit with Jesus Christ, from 1 Corinthians 6:17, we also know that our dear departed relatives who we miss so much are also present at every Mass we attend.
How is all of this possible? Because Jesus is God, and he can do anything! The entire Old Testament points to this miracle, whether it's Melchizedek offering bread and wine as sacrifice with Abraham; the Jews having to eat the spotless Passover Lamb to be saved from death (NOT A SYMBOL OF ONE!); the Jews being kept alive DAILY with supernatural bread from heaven in the desert, called manna (..."Give us this day our DAILY bread" from the Our Father prayer refers to the daily Mass/Eucharist); the changing of water into wine by Jesus at the wedding in Cana (a wedding is where 2 people become ONE FLESH!); and the feeding of the crowd in the desert by Jesus multiplying the loaves.
Some people erroneously believe that Catholics are sacrificing Jesus over and over again on the altar, which means that His one sacrifice wasn't quite good enough! But that is an error in their thinking. The Eucharistic sacrifice on every altar of every Catholic Church is done at the command of Jesus, in Luke 22:19, and it is the one and the same sacrifice RE-PRESENTED for us today through time and space (this is similar to a movie DVD re-presenting the same actors and the same words and the same scenes over and over again, even though it appears to be happening for the first time on your TV screen. The original set and the original acting are long gone, but they are re-presented for us today!), and every day, so that we can be saved from satan, who loves it when we eat his forbidden fruit. The Eucharist overcomes satan's 2 lies to Adam and Eve- "Ye shall not die," and "Ye shall be as gods," he told them, if they would partake of the forbidden fruit. By consuming the fruit of the tree known as the cross, called the Eucharist, we shall live forever (John 6:54), and we become one flesh with God (John 6:56)!
To deny that this can even happen is to deny the power of the Holy Spirit, the Love of God!
In the 16th Century, a lot of men came up with their own peculiar traditions of what they erroneously believed the Eucharist to be, some kind of "symbol," a word to be found nowhere in Scripture when describing the Eucharist. In reality, scripture says THIS about the Eucharist:
John 6:  I am the bread of life.
 Your fathers ate the manna in the wilderness, and they died.
 This is the bread which comes down from heaven, that a man may eat of it and not die.
 I am the living bread which came down from heaven; if any one eats of this bread, he will live for ever; and the bread which I shall give for the life of the world is my flesh."
The Jews then disputed among themselves, saying, "How can this man give us his flesh to eat?"
 So Jesus said to them, "Truly, truly, I say to you, unless you eat the flesh of the Son of man and drink his blood, you have no life in you; he who eats my flesh and drinks my blood has eternal life, and I will raise him up at the last day. (The Greek word here for "eats" means to "munch on", or to "gnaw on.")
 For my flesh is REAL FOOD, and my blood is REAL DRINK.(Notice how Jesus says the Eucharist is REAL FOOD and REAL DRINK, not symbolic food and drink!)
 He who eats my flesh and drinks my blood abides in me, and I in him.
 As the living Father sent me, and I live because of the Father, so he who eats me will live because of me.
 This is the bread which came down from heaven, not such as the fathers ate and died; he who eats this bread will live for ever."
And we have the words recorded from the successors to the apostles, like Ignatius, a martyr in the Colisseum of Rome who was taught by St. John the Apostle, which prove that Jesus wasn't talking in "symbolic" terms!
St. Ignatius of Antioch (110 A.D.)
I have no taste for corruptible food nor for the pleasures of this life. I desire the Bread of God, WHICH IS THE FLESH OF JESUS CHRIST, who was of the seed of David; and for drink I DESIRE HIS BLOOD, which is love incorruptible. (Letter to the Romans 7:3)
Take care, then, to use one Eucharist, so that whatever you do, you do according to God: FOR THERE IS ONE FLESH OF OUR LORD JESUS CHRIST, and one cup IN THE UNION OF HIS BLOOD; one ALTAR, as there is one bishop with the presbytery… (Letter to the Philadelphians 4:1)
They [i.e. the Gnostics] abstain from the Eucharist and from prayer, because they do not confess that THE EUCHARIST IS THE FLESH OF OUR SAVIOR JESUS CHRIST, flesh which suffered for our sins and which the Father, in his goodness, raised up again. (Letter to Smyrnians 7:1)
St. Justin the Martyr (100 - 165 A.D.)
We call this food Eucharist; and no one else is permitted to partake of it, except one who believes our teaching to be true and who has been washed in the washing which is for the remission of sins and for regeneration [Baptism], and is thereby living as Christ has enjoined.
For not as common bread nor common drink do we receive these; but since Jesus Christ our Savior was made incarnate by the word of God and had both flesh and blood for our salvation, so too, as we have been taught, the food which has been made into the Eucharist by the Eucharistic prayer set down by Him, AND BY THE CHANGE OF WHICH our blood and flesh is nourished, IS BOTH THE FLESH AND THE BLOOD OF THAT INCARNATED JESUS. (First Apology, 66)
Moreover, as I said before, concerning the sacrifices which you at that time offered, God speaks through Malachi [1:10-12]…It is of the SACRIFICES OFFERED TO HIM IN EVERY PLACE BY US, the Gentiles, that is, OF THE BREAD OF THE EUCHARIST AND LIKEWISE OF THE CUP OF THE EUCHARIST, that He speaks at that time; and He says that we glorify His name, while you profane it. (Dialogue with Trypho, 41)
St. Irenaeus of Lyons (140 - 202 A.D.)
…He took from among creation that which is bread, and gave thanks, saying, "THIS IS MY BODY." The cup likewise, which is from among the creation to which we belong, HE CONFESSED TO BE HIS BLOOD.
He taught THE NEW SACRIFICE OF THE NEW COVENANT, of which Malachi, one of the twelve prophets, had signified beforehand: [quotes Mal 1:10-11]. By these words He makes it plain that the former people will cease to make offerings to God; BUT THAT IN EVERY PLACE SACRIFICE WILL BE OFFERED TO HIM, and indeed, a pure one; for His name is glorified among the Gentiles. (Against Heresies 4:17:5)
But what consistency is there in those who hold that the bread over which thanks have been given IS THE BODY OF THEIR LORD, and the cup HIS BLOOD, if they do not acknowledge that He is the Son of the Creator… How can they say that the flesh which has been nourished BY THE BODY OF THE LORD AND BY HIS BLOOD gives way to corruption and does not partake of life? …For as the bread from the earth, receiving the invocation of God, IS NO LONGER COMMON BREAD BUT THE EUCHARIST, consisting of two elements, earthly and heavenly… (Against Heresies 4:18:4-5)
If the BODY be not saved, then, in fact, neither did the Lord redeem us with His BLOOD; and neither is the cup of the EUCHARIST THE PARTAKING OF HIS BLOOD nor is the bread which we break THE PARTAKING OF HIS BODY…He has declared the cup, a part of creation, TO BE HIS OWN BLOOD, from which He causes our blood to flow; and the bread, a part of creation, HE HAS ESTABLISHED AS HIS OWN BODY, from which He gives increase to our bodies.
When, therefore, the mixed cup and the baked bread receives the Word of God and BECOMES THE EUCHARIST, THE BODY OF CHRIST, and from these the substance of our flesh is increased and supported, how can they say that the flesh is not capable of receiving the gift of God, WHICH IS ETERNAL LIFE -- flesh which is nourished BY THE BODY AND BLOOD OF THE LORD…receiving the Word of God, BECOMES THE EUCHARIST, WHICH IS THE BODY AND BLOOD OF CHRIST… (Against Heresies 5:2:2-3)