Since the first century of her existence, the Church has considered the Mass a sacrifice. The earliest manual of the liturgy (before 90 A.D.) has this directive for the attendance of Sunday Mass.
"On the Lord's own day, assemble in common to break bread and offer thanks. But first confess your sins so that your sacrifice may be pure. (Teaching of the Twelve Apostles, 14)."
Why is the Mass a true sacrifice? Because in the Mass the same Jesus Christ who offered Himself on Calvary now offers Himself on the altar. The Priest is the same, the Victim is the same, and the end or purpose is the same.
The Priest is the same Jesus Christ whose sacred person the ordained priest represents and in whose Name he offers the Eucharistic Sacrifice.
The Victim is the same, namely the Savior in His human nature, with His true Body and Blood, and His human free will. Only the manner of offering is different. On the Cross, the sacrifice was bloody; in the Mass it is unbloody because Christ is now in His glorified state. But the heart of sacrifice is the voluntary, total offering of oneself to God. Christ makes this voluntary offering in every Mass, signified by the separate consecration of the bread and wine into the Body and Blood of the Redeemer.
The end or purpose is the same, namely to give glory to God, to thank Him, to obtain His mercy, and to ask Him for our needs. But, as we have seen, whereas on Calvary Christ merited our salvation, it is mainly through the Mass that He now dispenses the riches of His saving grace.
(Source)