The Mass is…

The unbloody sacrifice of the New Law, in which the Body and Blood of Christ, under the species of bread and wine, by a mystical immolation, are offered by a legitimate minister of Christ to God in order to acknowledge His supreme dominion and to apply to us the merits of the Sacrifice of the Cross.

^{—B. Merkelbach, O.P., Summa Theologiæ Moralis (vol. 3), 8th ed. (Montreal: Desclee 1949) 3:308, quoted in Anthony Cekada, Work of Human Hands: A Theological Critique of the Mass of Paul VI pp. 105-6}

357. What is the Mass?
     The Mass is the sacrifice of the New Law in which Christ, through the ministry of the priest, offers Himself to God in an unbloody manner under the appearances of bread and wine.

^{—The New Saint Joseph Baltimore Catechism (no. 2) p. 168}

^EUCHARIST

^{The true Body and Blood of Jesus Christ, who is really and substantially present under the appearances of bread and wine, in order to offer himself in the sacrifice of the Mass and to be received as spiritual food in Holy Communion. It is called Eucharist, or "thanksgiving," because at its institution at the Last Supper Christ "gave thanks," and by this fact it is the supreme object and act of Christian gratitude to God.}

^{Although the same name is used, the Eucharist is any one or all three aspects of one mystery, namely the Real Presence, the Sacrifice, and Communion. As Real Presence, the Eucharist is Christ in his abiding existence on earth today; as Sacrifice, it is Christ in his abiding action of High Priest, continuing now to communicate the graces he merited on Calvary; and as Communion, it is Christ coming to enlighten and strengthen the believer by nourishing his soul for eternal life. (Etym. Latin eucharistia, the virtue of thanksgiving or thankfulness; from Greek eucharistia, gratitude; from eu-, good + charizesthai, to show favor.)}

^{—Fr. Hardon, S.J., Catholic Dictionary}

Does the Catholic Church have a formal definition of the Mass?

A Catholic definition of the Mass needs a explanation in order that it be truly understood.

Here is how Fr. Hardon SJ defines the Mass:

Mass

The Sacrifice of the Eucharist as the central act of worship of the Catholic Church. The "Mass" is a late form of missio (sending), from which the faithful are sent to put into practice what they have learned and use the graces they have received in the Eucharistic liturgy.

As defined by the Church at the Council of Trent, in the Mass, "The same Christ who offered himself once in a bloody manner on the altar of the cross, is present and offered in an unbloody manner." Consequently, the Mass is a truly propitiatory sacrifice, which means that by this oblation "the Lord is appeased, He grants grace and the gift of repentance, and He pardons wrongdoings and sins, even grave ones. For it is one and the same victim. He who now makes the offering through the ministry of priests and he who then offered himself on the cross. The only difference is the manner of offering" (Denzinger 1743).

The Mass cannot be understood apart from Calvary, of which it is a re-presentation, memorial, and effective application of the merits gained by Christ.

The re-presentation means that because Christ is really present in him humanity, in heaven and on the altar, he is capable now as he was on Good Friday of freely offering himself to the Father. He can no longer die because he now has a glorified body, but the essence of his oblation remains the same.

The Mass is also a memorial. Christ's death is commemorated not only as a psychological remembrance but as a mystical reality. He voluntarily offers himself, the eternal high priest, as really as he did on Calvary.

The Mass is, moreover, a sacred banquet or paschal meal. The banquet aspect of the Mass is the reception of Holy Communion by the celebrant and the people, when the same Christ who offers himself to the Father as a sacrifice then gives himself to the faithful as their heavenly food. It was this fact that inspired the Holy See, after the Second Vatican Council, to restore the practice of receiving Communion under both kinds for all the faithful: "The entire tradition of the Church teaches that the faithful participate more perfectly in the Eucharistic celebration through sacramental Communion. By Communion, in fact, the faithful share more fully in the Eucharistic Sacrifice. In this way they are not limited to sharing in the sacrifice by faith and prayer, nor to merely spiritual communion with Christ offered on the altar, but receive Christ himself sacramentally, so as to receive more fully the fruits of this most holy sacrifice. In order that the fullness of the sign in the Eucharistic banquet may be seen more clearly by the faithful, the Second Vatican Council prescribed that in certain cases, to be decided by the Holy See, the faithful could receive Holy Communion under both species" (Sacramentali Communione, June 29, 1970).

Finally the Mass is the divinely ordained means of applying the merits of Calvary. Christ won for the world all the graces it needs for salvation and sanctification. But these blessings are conferred gradually and continually since Calvary and mainly through the Mass. Their measure of conferral is in proportion to the faith and loving response of the faithful who unite themselves in spirit with the Mass.

It is in this sense that the Mass is an oblation of the whole Mystical Body, head and members. Yet, among the faithful, some have been ordained priests and their role in the Mass is essentially different from that of the laity. The priest is indispensable, since he alone by his powers can change the elements of bread and wine into the body and blood of Christ. Nevertheless the role of the participants is of great importance; not as though there would be no Mass without a congregation but because the people's "full, active and conscious participation will involve them in both body and soul and will inspire them with faith, hope and charity." The more active this participation, the more glory is given to God and the more grace is bestowed not only on the Church but on all the members of the human race.