What's the Catholic Church's View?
The existence of Purgatory or a 'purifying process' after death is a Catholic Dogma of the Faith which means every Catholic must believe in order to remain a Catholic. The Church does not insist that it is a place, but may be a process only. It is not a destination ~ but a sort of passage through which all who must experience it, will eventually be purified enough to see God face to face.
It's understood that the souls undergoing this purification may benefit from the prayers of the living, but that the opportunity of grace to pray for their own relief has passed.
Just as a prisoner who awaits his trial - may be released from jail by a friend who pays the cost of his bail. So we may help to gain the release of a holy soul from the prison of his suffering. It's considered a great act of spiritual mercy by the Church to pray for the dead.
Catechism courtesy of Leaflets of Faith:
1030 - All who die in God's grace and friendship, but still imperfectly purified, are indeed assured of their eternal salvation; but after death they undergo purification, so as to achieve the holiness necessary to enter the joy of heaven.
1031 - The Church gives the name Purgatory to this final purification of the elect, which is entirely different from the punishment of the damned.
The Church formulated her doctrine of faith on Purgatory especially at the Councils of Florence (1439) and Trent (1563). The tradition of the Church, by reference to certain texts of Scripture, speaks of a cleansing fire:
"But if someone's work is burned up, that one will suffer loss; the person will be saved, but only as through fire." (I Cor 3:15)
"That the trial of your faith (much more precious than gold which is tried by the fire) may be found unto praise and glory and honor at the appearing of Jesus Christ:" (1 Peter 1:7)