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From the beginning of the world the servants of God were always accustomed to offer Sacrifice to Him, by way of acknowledging His sovereignty and paying their homage to Him ; and in all ancient religions, true or false, this worship of Sacrifice was always regarded as a most solemn act of religion, due to the Deity worshiped.

In the law of nature, and in the law of Moses, there was a great variety of Sacrifices : some bloody, in which the victim was slain ; others unbloody. Some were called Holocausts, or whole burnt-offerings, in which the whole host or victim was consumed in fire upon God’s altar, for His honor and glory : others were called Sin-offerings, which were offered for sins ; others were offerings of Thanksgivings ; others were pacific or Peace-offerings, which were offered for obtaining favors of God— the word “ peace ” in the Scripture style signifying all manner of good and prosperity.

All these Sacrifices of the law of nature, and of the law of Moses, were of themselves but weak and needy elements (Gal. IV. 9), and only figures of a Sacrifice to come, viz., that of Jesus Christ; in consideration of which Sacrifice only, and of the faith of the offerers, by which they believed in the Redeemer to come, those ancient Sacrifices were then accepted by the Divine Majesty, when they were accompanied with the inward sacrifice of the heart; but not for any intrinsic worth or dignity of the things offered, for no other blood but the Blood of Christ could wash away sins. Hence, St. Paul says (Heb. x . 5), quoting from the 39th Psalm : Sacrifice and oblation Thou wouldst not have : but Thou hast fitted to Me a Body. This gives us to understand that, by reason of the insufficiency of the Sacrifices of the old law, Christ Himself would come to be our Sacrifice, and would offer up His own Body and Blood for us.

Accordingly, our Savior Jesus Christ, at the time appointed by His Father, having taken flesh for us, was pleased to offer Himself a Sacrifice for us, dying upon the Cross for the sins of the whole world. By this one offering we were completely redeemed, inasmuch as our ransom was paid, and all mercy, grace, and salvation were purchased for us. Neither can there now be any need of His dying any more, or purchasing any other graces for us than those for which He has already paid the price of His Blood.

Nevertheless, for the daily application of this one eternal Redemption to our souls, and that the mercy, grace, and salvation which He has purchased for us may be actually communicated to us, He not only continually appears in our behalf in the Sanctuary of Heaven, there representing and offering to His Father His Passion and Death for us, but He has also instituted the Blessed Eucharist, the night before His Passion, in which He bequeathed us His Body and Blood, under the sacramental veils, not only to be received by us as a Sacrament, for the food and nourishment of our souls, but also (mystically delivered) to be offered and presented by His ministers to His Father as a Sacrifice : not by way of a new death, but by way of a standing Memorial of His death ; a daily celebrating and representing of His death to God, and an applying to our souls of the fruits thereof.

This Eucharistic Sacrifice of the Body and Blood of Christ, daily offered under the forms of bread and wine, in remembrance of His Passion, is what we call the Mass. This is the solemn Liturgy of the Catholic Church. This is that pure Offering which is made to God in every place among the Gentiles, according to the prophecy of Malachi (I. 10 , 11). By this, Christ is a Priest for ever according to the order of Melchizedek (Psalm 109), whose Sacrifice was bread and wine (Gen. xv.)

This Sacrifice of the Mass is the same in substance with that which Christ offered for us upon the Cross; because both the Victim offered, and the Priest or principal Offerer, is the same Jesus Christ. The difference is only in the manner of the offering ; because upon the Cross our Savior offered Himself in such a manner as really to shed His Blood and die for us ; whereas now He does not really shed His Blood, or die. And therefore this is called an unbloody Sacrifice; and that of the Cross a bloody Sacrifice.

By virtue of this essential sameness, the Sacrifice of the Mass completely answers all the different ends of Sacrifice, and that in a way infinitely more effective than any of the ancient Sacrifices. Christ is here both Priest and Victim, representing in person and offering up His Passion and Death to His Father.

This Sacrifice of the Mass is offered up to God, in the Catholic Church, first as a daily remembrance of the Passion of Christ: This do for the commemoration of Me (I Cor. XI. 24) ; secondly, as a most solemn worship of the Divine Majesty ; thirdly, as a most acceptable thanksgiving to God, from whence it has the name of Eucharist ; fourthly, as a most powerful means to move God to show mercy to us in the forgiveness of our sins, for which reason we call it propitiatory ; and, lastly, as a most effectual way to obtain of God all that we need, coming to Him, as we here do, with Christ and through Christ.

For these ends both Priest and people ought to offer up the Sacrifice of the Mass — the Priest, as Christ’s minister and in His person ; and the people, by the hands of the Priest ; and both the one and the other by the hands of the Great High-Priest Jesus Christ. And with this offering of Christ, both the one and the other should make a total offering of themselves also by His hands and in union with Him. 

Source: A Manual Of Prayers For The Use Of The Catholic Laity: Prepared And Published By Order Of The Third Plenary Council Of Baltimore 1888