What's the first thing that comes to mind when I say the word, "suffrages?" I bet you are thinking along the lines of voting. I think of the women suffragettes who fought for the right to vote. but the first, or earlier meaning of the word is "prayers."
There is a relationship. Suffering is involved in asking for voting rights and prayers for the suffering is asking God for help. That is the original meaning.
From the Catholic Dictionary:
The prayers prescribed or promised for specific intentions. More particularly, suffrages are the Masses, prayers, or acts of piety offered for the repose of the souls of the faithful departed.
and this site quotes the Summa Theologica:
71. Suffrages for the Dead
1. The word suffrage really means a vote.A suffrage is a vote, or a request to God, that some good actof ours have its merit bestowed on another. A suffrage is a gooddeed cast, like a ballot, in favor of someone. All the faithful aremembers of one body which is the Church. And, as in a living body,one member may be assisted by another. Such assistance is asuffrage. So much we know from the doctrine called the"Communion of Saints." But one member cannot actuallyreplace another; one member of the Church cannot save the soul ofanother. One member may, and should, help another, not only bygiving him good example and praying for him, but by performing goodand meritorious deeds, and ascribing the benefit of these toanother.
2. The prayers and suffrages of the living, offered forthe souls in purgatory, are of benefit to these souls. This we knowfrom the infallible teaching of the Church, and also from scripture(II Machabees 12:46): "It is a holy and wholesome thought topray for the dead that they may be loosed from theirsins."
3. Even those who are in the state of mortal sin may dosomething for the souls in purgatory. For the deed donemay have a value apart from the status of the doer of thedeed.
4. Suffrages offered by the living on behalf of the soulsin purgatory are deeds of charity, and, as such, they confer abenefit upon those who perform them. Says Psalm 34: "My prayershall be turned into my bosom."
5. Suffrages, however, can be of no benefit whatever tothose who are in hell. The lost souls are changelessly beyond allaid. They are under debt of eternal punishment, and no suffragewith its gift of temporal satisfaction, can be of any avail.
6. It is a point of the faith itself that the suffrages ofthe living help the souls in purgatory to pay their temporal debt.For purgatory does the work of satisfaction that a person couldhave done in this life, but died without doing, or withoutcompleting. Temporal punishment can be paid off; we on earth canhelp pay it for our brethren in purgatory who can merit no longerfor themselves.
7. Infants in Umbo cannot be aided by suffrages. For theseinfants are not under any debt of punishment for actual sins. Wecannot relieve temporal suffering where there is no suffering torelieve.
8. Suffrages are called so because they help,just as a vote helps toelect a man. Now, we cannot help thosewho have achieved the glory of heaven. One cannot help another toget home if he is already at home. So we do not offer suffrages onbehalf of the saints.
9. The Holy Sacrifice of the Mass, the share we have inthe general prayer of the Church, and almsgiving, are notable worksof charity; therefore, these are powerful suffrages.
10. Indulgences granted by the Church and made applicableto the souls in purgatory can be gained by the faithful on earthfor the benefit of the holy souls. And indulgences thus gained aresuffrages.
11. St. Augustine says that the burial service for thedead, with its solemn ceremonies, is rather a consolation for thesurvivors than a help for the departed. And yet the burial serviceas prescribed by the Church contains many prayers for the dead, andeven Holy Mass which is offered for the departed soul. Further, theceremonies themselves may stir observers to pious thoughts, andlead them to pray and offer suffrages for the dead. And thus,"to bury the dead," is indeed a work of mercy. And assuch a work, it is a suffrage.
12. It seems most reasonable to suppose that suffragesoffered for one definite person are a help to him rather than toanother who is perhaps more worthy of help. For the suffrageoffered derives its value not only from the deed done, but from theintention of the doer of the deed.
13. Suffrages offered for several souls are divided amongthe souls. It is quite unreasonable to think or say, as some havedone, that such suffrages are of as much value for each of theseveral souls as if they were offered for that one soul alone.
14. General suffrages (those offered in general for thesouls in purgatory) are certainly of profit to the holy souls. Buthere again it is unreasonable to say that neglected souls find ingeneral suffrages such help as makes up to them all they have beendeprived of through neglect on the part of those who should helpthem.
