Certainly, one Catholic doctrine that is often denied is the reality and existence of purgatory. The existence of Purgatory is an article of faith. This means that anyone who doubts or denies the existence of purgatory has departed from Catholic orthodoxy. Purgatory is a place or condition in which the souls of the just are purified after death before they enter heaven.
Because of the holiness of God nothing unclean can enter into his presence. After death, there are, we know from revelation and Church teaching, only two eternal and irrevocable possibilities: heaven or hell. Those in the state of sanctifying grace who have no taint of sin on their souls go to heaven, while those who die in the state of mortal sin go to hell.
But there is a third possibility for those who die in the state of sanctifying grace but carry with them unrepented venial sins or the temporal punishment due to forgiven mortal sin for which satisfaction has not yet been made by prayer and penance. Since they are "unclean" they cannot enter heaven; since they possess sactifying grace they do not deserve hell. The Church says that they must spend a certain amount of time in purgatory and make adeequate satisfaction for their sins before going to heaven.
Many in the Middle Ages, as well as Protestant reformers, denied the reality of purgatory owing to their erroneous view of justification. The 2nd Council of Lyon (1274) affirmed the teaching on purgatory. "If those who are...penitent die...before they have done sufficient penance for their sin...their souls are cleansed after death in purgatorial or cleansing punishments...The suffrages of the faithful on earth can be of great help in relieving these punishments, as for instance, the Sacrifice of the Mass, prayers, almsgiving, and other religious deeds." This was reaffirmed by the Council of Florence and Vatican II.
Scriptural evidence is for the most part, indirect but does admit the possibilitiy of purification in the next world. (2 Macc 12: 42-46). Many Church Fathers interpreted Christ's words in Matthew 12:32 as referring to purification in the next life. See also: Matt 5:26 and 1 Cor 3:12.
Although the poor souls are assured of salvation, since they need cleansing, they are separated from God for a time. We are not certain about the nature of the punishment or cleansing of purgatory. The Church does not teach dogmatically that there is a physical fire even though this is sometimes read. The sufferings of purgatory would not be the same for all but are proportioned to each one's degree of sinfulness.
It is the Church's teaching that the sufferings of the poor souls can be alleviated by the prayers and penances of the faithful on earth. This is why we are urged to pray for them, to suffer for them, and to offer up Masses for them. The pains of purgatory are accompanied by great peace and joy because the poor souls love God and know for certain that they will eventually reach heaven.
One of the consoling aspects of the doctrine of he communion of saints is that there is a community among all Christ's faithful--those on earth, those in purgatory and those in heaven. This means that the faithful on earth can assist the souls in purgatory by offering for them prayers, alms, and sufferings, and especially the Holy Sacrifice of the Mass.
Since Protestants do not believe in purgatory and seem to assume that Christians who die go directly to heaven, in their funerals they do not pray for the deceased. Rather, they pray for he surviving members of the deceased's family and friends. The Catholic practice in time of mourning is different. Catholics pray for the "repose of the soul" of the deceased, offering God Masses and prayers. This practice can be traced back to at least the 2nd century.
In the Old Testament we find the belief that those who had died with some sin on their would could be helped by prayer and sacrifices of atonement. We read in 2 Mac 12:41-45 that Judas Maccabeus had prayers and sacrifices offered to God for his fallen soldiers: Christians then took over from Judaism this belief. Ancient Christian tomb inscriptions from the 2nd and 3rd centuries frequently appeal for prayers for the dead.
The 2nd Council of Lyons finally codified this thousand year belief in 1274: "If those who are... penitent die...before they have done sufficient penance for their sin...their souls are cleansed after death in purgatorial or cleansing punishments... The suffrages of the faithful on earth can be of great help in relieving these punishments, as for instance, the Sacrifice of the Mass, prayers, almsgiving and other religious deeds." This was reaffirmed by the Council of Florence and Vatican II.
Prayers for he souls in purgatory are often called "suffrage"--a word derived from the Latin suffraginium which means "supplication." The way that suffrages work is that the satisfactory value of prayers and good works is offered to God in substitution for the temporal punishments for sins, which the poor souls still have to render. God accepts the offering and remits all or a portion of the temporal punishments due to sins--depending on the spiritual value of the offering and on the disposition of the one making the offering.
While saints in heaven can no longer gain merits before God as we can, they can also help the souls in purgatory by their prayers that he have mercy on the poor souls.
Since the poor souls are members of the Mystical Body and are assured of salvation, the question has been raised about whether or not they can intercede for other suffering souls and for the faithful on earth. Theologians have been divided on the point but there is an old custom of invoking the help of the souls in purgatory. The Church does not encourage the practice, but she has also never condemned it. This means that one may, in good conscience, not only pray for but also to the poor souls.