Today we tend to think of the Mass merely in terms of communal worship, which it is in part, but the Mass is first and foremost a sacrifice offered by a priest, i.e. something that renders God his due and obtains his favor. How is this possible, since God is infinite in majesty and we are mere creatures? It is possible because Jesus is God Incarnate, and His sacrifice on the cross was infinite in value.
The merits and fruits of Jesus’ sacrifice are applied to us through the Mass. Since we are limited beings, we cannot receive infinite spiritual fruits all at once, so the Mass is offered again and again. In addition to the general intentions of adoration, thanksgiving, expiation, and supplication, the priest also applies each Mass to a specific person or intention. That is what a “Mass intention” is. You can and should have your own, private intentions and unite them with the Sacrifice, but this is not the principal intention of the Mass, which is offered by the priest alone as God’s representative.
There’s no strict formula for a Mass intention; it is primarily an act of will on the part of the priest; but it is useful for the priest to have it written down to remind him, e.g. “John Smith, R.I.P.”; “for vocations”; “special intention for Suzie Q.”. You can submit such an intention to the parish office, or to the priest himself. It is customary to give a stipend (in my diocese it is customary to contribute $10 per Mass), not to pay for the sacrifice, but as a way of participating in the sacrifice, and also for the support of the priest.
As to reliable sources, there’s a good summary in: Fr. Hardon’s
Modern Catholic Dictionary (click the drop-down and select Mass Intention). Regarding the Sacrifice of the Mass generally, see the
Catholic Encyclopedia article.
Baltimore Catechism III sums up the essentials:
Q. 923. How are the fruits of the Mass distributed?
A. The fruits of the Mass are distributed thus:
- The first benefit is bestowed on the priest who says the Mass;
- The second on the person for whom the Mass is said, or for the intention for which it is said;
- The third on those who are present at the Mass, and particularly on those who serve it, and
- The fourth on all the faithful who are in communion with the Church.
Q. 926. For what end or intention may Mass be offered?
A. Mass may be offered for any end or intention that tends to the honor and glory of God, to the good of the Church or the welfare of man; but never for any object that is bad in itself, or in its aims; neither can it be offered publicly for persons who are not members of the true Church.
Q. 929. From what did the custom of making an offering to the priest for saying Mass arise?
A. The custom of making an offering to the priest for saying Mass arose from the old custom of bringing to the priest the bread and wine necessary for the celebration of Mass.
Q. 930. Is it not simony, or the buying of a sacred thing, to offer the priest money for saying Mass for your intention?
A. It is not simony, or the buying of a sacred thing, to offer the priest money for saying Mass for our intention, because the priest does not take the money for the Mass itself, but for the purpose of supplying the things necessary for Mass and for his own support.