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There are white ‘Mass Offering’ envelopes in the porch: please write your intention on the outside of the envelope, enclose your Mass stipend donation, and place the envelope in the parish secretary's letterbox.
What is a Mass Intention?
What does it mean to have a Mass offered ‘for’ something or someone? In answering this question it is important to differentiate between the general and particular intentions in the Mass: Every Mass is offered with the general intention that is articulated in every Eucharistic Prayer: for the glory of God and for the needs of the Church and the world as a whole. In addition, each individual member of the congregation brings his or her own particular intentions in his or her prayers that are united to that Mass. There is a third type of intention brought to the Mass, however, and it is this intention that is referred to when people speak of a ‘Mass Intention’, namely, the specific intention for which the priest celebrant offers the Mass: The priest’s intention specifies the “special fruit” for which that particular Mass is being offered. It is in this sense that someone asks a priest to offer Mass ‘for’ something or someone.
Linked with the above is the ancient practice of Mass Stipends: a financial offering to accompany the offering of your prayer, a specific donation to accompany the specific request. While the amount donated for a Mass is at the discretion of the individual there is a standard rate set in each diocese and for many years our Bishop has set this at £10. In this parish the donation goes to the parish funds (in contrast, most other places continue the ancient practice of the Mass offering going to support the priest).
The Mass is the greatest prayer we have since it is the sacrifice of Christ Himself. It is therefore important to remember that we can have Mass offered for many intentions: for the living as well as for the dead, for family difficulties, for sickness, as well as in thanksgiving for graces received etc. Even a casual glance over the list of Mass intentions being offered in any parish will show the wide range of intentions people bring.
Masses for the Dead
The most common type of Mass intention people that request is for someone who has died. The practice of offering Masses for the dead is the Christian fulfilment of the Jewish practice of having sacrifices offered in the Temple for the dead “so that they might be released from their sins” (2 Macc 12:45). The Early Church celebrated the Holy Sacrifice of the Mass as the sacrifice that superseded the Old Testament Temple sacrifices and it was for this reason that the writings of the Early Church Fathers record how the Mass was offered for the dead. For example, Tertullian writes in the 2nd Century about a widow who had Mass offered for her deceased husband: "Indeed she prays for his soul, and requests refreshment for him meanwhile, and fellowship with him in the first resurrection; and she offers her sacrifice on the anniversaries of his falling asleep". Similarly, many of the Fathers echo the sentiment expressed by St Gregory the Great, "Let us not hesitate to help those who have died and to offer our prayers for them." While St. John Chrysostom encourages us by saying, "If Job's sons were purified by their father's sacrifice, why would we doubt that our offerings for the dead bring them some consolation? Let us not hesitate to help those who have died and to offer our prayers for them." 
The month of November is a time when people particularly remember to have Masses offered for the dead, especially for family and friends.
Announcing the intention?
In our parish, the intention of each Mass is published in the weekly newsletter as well as appearing on the parish website. In some parishes intentions are published on a notice board and in some places the priest may announce the intention, especially if it is a change to the one published.
It is worth noting, however, that the offering of the Mass for that intention does not depend on it being publically voiced but on it being specified in the priest’s personal prayers. Similarly, if a priest announces that “I am offering this Mass for [such and such an] intention” he does not thereby require the rest of the congregation to pray for that intention or to make their own lay-offering of the Mass to be for that intention. The priest’s intention specifies the “special fruit”  chosen as his intention it does not specify that of the congregation. Therefore, to avoid the impression of the priest imposing his intention on the rest of the congregation many priests avoid announcing the intention.
See also an article at EWTN here
A more thorough theological analysis in the 1950s classic work, O'Connell's The Celebration of the Mass, can be viewed here
 Pope Pius VI, Auctorem Fidei (1786), cited in Aidan Nichols, The Holy Eucharist (Dublin: Veritas, 1991), p.100.
 Fr William Saunders, “What does it mean to have a Mass ‘offered’ for someone?”,
 As cited in .