The Mass is a mysteriously spiritual experience that not only unites us with the Church on earth, but also to all those suffering souls in purgatory.
Souls of the deceased in purgatory are not cut off from the Body of Christ, but are still part of the Church, though they are not yet fully united to God in eternal splendor.
Peace of Christ
The Church has taught for many centuries that our prayers at Mass for the dead can help them complete their "time" in purgatory.
The Catechism of the Catholic Church summarizes this teaching in its section on the Eucharist:
The Eucharistic sacrifice is also offered for the faithful departed who "have died in Christ but are not yet wholly purified," so that they may be able to enter into the light and peace of Christ
The Catechism then quotes the 4th-century bishop St. Cyril of Jerusalem to help affirm this teaching:
Then, we pray [in the anaphora] for the holy fathers and bishops who have fallen asleep, and in general for all who have fallen asleep before us, in the belief that it is a great benefit to the souls on whose behalf the supplication is offered, while the holy and tremendous Victim is present.... By offering to God our supplications for those who have fallen asleep, if they have sinned, we . . . offer Christ sacrificed for the sins of all, and so render favorable, for them and for us, the God who loves man.
One miraculous example of the power of the Mass is found in a story about a grieving young girl who approached Benedictine Abbot Millán de Mirando at the monastery of Our Lady of Montserrat. She begged the abbot to say three Masses for her deceased father.
At the third Mass offered for the repose of her father's soul, she saw her father for the last time. During the Eucharistic celebration he was "dressed in a snow-white suit," but then something extraordinary happened at the conclusion of Mass. The little girl exclaimed, "There is my father going away and rising into the sky!" She no longer had to worry about the soul of her father as she knew with confidence that he had reached the gates of heaven.
Offering Mass for the dead is a long-standing tradition in the Catholic Church, one that connects us to the Church Suffering and helps speed them on to the gates of Heaven.