The Mass is a sacrifice because it renews the Sacrifice of Christ on the Cross and applies its saving grace to our lives (Catechism of the Catholic Church, no. 1366). In a particular way, the grace of Mass is applied to specific needs (for example, a person living or deceased) by means of a Mass intention.
According to Church law, at least one Mass on Sunday or holy day of obligation (celebrated during the day or the evening prior) must be offered “for the people” (in Latin: pro populo) (Code of Canon Law, canons 388, 534).
Aside from the pro populo requirement, Masses may be offered for other intentions (usually one intention per Mass, either on Sunday or a weekday). It is customary—but not required—for members of the faithful to provide a stipend for the priest when a Mass intention is offered (canon 945 §1). The stipend is a way to contribute toward the financial support of the clergy of the Church (canon 946), and to unite oneself more closely to Christ, who is the Victim offered in the Mass (Pope Paul VI, Apostolic Letter on Faculties Concerning Mass Stipends, Firma in traditione [1974]). The stipend should never be thought of as “purchasing” a Mass. The customary stipend is $5.00 per Mass.