What is the Catholic sacrament of Holy Eucharist? What is the Catholic definition of celebrating Holy Eucharist?

We cannot do better than to take the definition of Transubstantiation given by the Council of Trent; that "This holy Synod now anew declares, that by the consecration of the bread and wine, conversion of the whole substance into the substance of the body of Christ our Lord takes place, and of the whole substance of the wine into the substance of His blood. Which conversion is conveniently and properly called by the holy Catholic Church, "Transubstantiation." An anathema is pronounced against anyone who denies "that in the sacrament of the most holy Eucharist are contained truly, really, and substantially, the body and blood together with the soul and divinity of our Lord Jesus Christ, and consequently a whole Christ." The catechism of the same Council declares that, "Not only the true body of Christ, and whatever belongs to the true body, as bones and nerves, but also a whole Christ," is contained in the sacrament. It is said that the whole substance of the bread is converted into the body, and the whole substance of the wine into the blood; only the forms of bread and wine remaining, and it is to be adored with divine worship.

"I profess likewise, that in the mass is offered to God a true, proper, and propitiatory sacrifice for the living and the dead; and that, in the most holy sacrifice of the Eucharist, there is truly, really, and substantially, the body and blood, together with the soul and divinity of our Lord Jesus Christ; and that there is made a conversion of the whole substance of the bread into the body, and of the whole substance of the wine into the blood, which conversion the Catholic church calls transubstantiation.

Mass is offered daily in every Catholic parish, and many Catholics take part daily or several times a week. The Catechism states that the Eucharist is a memorial of Christ's passover but also a sacrifice. Christ gives participants in Eucharist the very body that He gave up for mankind on the cross and the very blood that He poured out for the forgiveness of sins. [.]

When the Catechism speaks of Christ being "offered in an unbloody manner," it means that during the Mass, Christ is not suffering and dying again. [.] Instead, His great moment of sacrifice is re‑presented so that Catholic believers can be part of it.

The Roman Catholics hold that after the priest has pronounced certain words over the bread and wine, they become changed into the actual body and blood of the Lord Jesus Christ. This is called transubstantiation. They also hold that both the body and blood of Christ are present in the bread which alone is given to the recipient, who thus partakes of the body and blood of Christ altogether independently of whether he has faith or not.

The Council of Trent has defined the Mass as "A propitiatory sacrifice available for the sins not only of the living but of the dead—truly propitiatory. Christ is unbloodily immolated there"; and the Catechism of the Same Council says: "The Mass is and ought to be considered one and the same sacrifice with that of the cross, for the victim is one and the same. . . . The bloody and unbloody are not two but only one victim whose sacrifice is daily renewed in the Eucharist. .. . . The priest is also one and the same, Christ the Lord."

So in the Lord's Supper we proclaim the Lord's death (1 Cor. 11:26), and hence in remembrance of Him we eat His body and drink His blood. Both are therefore sacraments of His death, not of Incarnation, as they wrongly say, wholly departing from God's mind. It is His body given (even if "broken" be rejected), His blood shed. This is not life, but death. And the difference is immense. For till Christ's death there was no bearing of our sins, no glorification of God about our evil, no redemption of the slaves of Satan. Both these divine institutions are grounded on that death of the Saviour which alone has brought us to God and reconciled us by a perfect atonement. The self-styled Catholic idea is essentially false, for it expresses no more than Incarnation at best, when the only work which could blot out our sins righteously was not done, but only in hope. And such is the spiritual experience generated by the error. They do not possess the joy of accomplished redemption. They have, as they say, a humble hope. But this is Jewish, not christian: quite right when our Lord was simply incarnate, and under the law; utterly and unbelievingly wrong now that He has died for our sins and is raised for our justification, having by one offering perfected for ever — without an interruption, εἰς τὸ διηνεκές — those that are sanctified, which all believers are. It is not the open hostile scepticism that denies the Incarnate Word; but it is real incredulity as to our present resting-place on His work as well as person, as set forth in both sacraments.

There is another antichristian doctrine, common (it is true) to the sacerdotal system of all ritualists, on which it may be well to say a little — the notion of offering up Christ's body and blood to God in the eucharist. No doubt, Popery goes farther in the deadly evil both by the fable of transubstantiation (which naturally if not necessarily leads to direct idolatry) and by claiming for the offering the character of a true propitiatory sacrifice for the living and the dead. But, even in the most modified shape, any offering to God of the sacrament is not only opposed to all scripture but destroys the truth of its proper nature and aim. The appeal to the original of 1 Cor. 11:24 and Matt. 26:28 ("now" broken and "now" shed) is mere ignorance in Mr. Cardale (Readings upon the Liturgy, p. 32). It is the present participle, not of time, but of character, whenever the time might be, like John 1:29 and crowds of instances. He Whom God made sin for us sits at God's right hand, Who needs no memorial of that perfect and accepted propitiation for our sins. This memorial He has made His Supper to be to us and our forgetful hearts. It is not for a moment to be doubted too that He is in the midst of His own when gathered to His name, and in the happiest way for this holy feast. Such is His true and only real presence. That it is in the bread and the wine is a baseless and base idea, not worthy of a Jew or even a pagan. We are there invited to eat and to drink. It is in no way an offering of His body and blood, but communion with both: just as Jews partook of what had been sacrificed, and Gentiles too in their dark way. But our God is love as well as light, and gives us to sit at a feast on the great sacrifice of Christ's redemption. Thereupon Christ sits on high, because it is done once for all, as its efficacy endures for ever, and even its application. There is no repetition. If there were renewed offering, there must be renewed suffering (Heb. 9:26). But it is finished; and we feast with thanksgiving and praise, doing this in remembrance of Him, and showing forth His death till He come. Presentation before God is a vain addition which spoils the revealed intent; and so does the mixing up our worship with Christ's priestly intercession, which has another and wholly distinct object.

N*. I have all Christ's institution, and a most blessed one too. That which we do, as He told us to do in remembrance of Him, and find grace and refreshment, comfort and sanctifying power from Himself in doing it, to say nothing of the deep thanksgiving and deeper affections it awakens in us. I hold it to be as to institutions, the highest privilege. That is not the question, but this conversion of bread and wine into the body and blood of Christ, His soul and divinity being there, and as I quoted, and the catechism of the Council of Trent says, His bones and nerves.

D. But I would not deny the efficacy of Christ's one sacrifice. The Mass, as you know, as held, is that same sacrifice, and the church by the Eucharist applies the benefit of it.

It describes the underground propaganda of Newman, Faber, Keble, Pusey, Manning, Ward, Mozley, Froude and others. It was not long before the doctrine of Transubstantiation was introduced; that is, in the celebration of the Lord’s Supper, it is blasphemously affirmed, that when the officiating priest pronounces certain words the bread and wine cease to be bread and wine, though in sight, taste and touch they appear to be such, and become the very flesh and blood of the Lord. This is called in Romish and Anglo-Catholic circles the Celebration of the Mass.