Purgatory, then, is that state where the soul resides after death until the soul is cleansed of all stain of sin.

The Catechism of the Catholic Church (CCC) has this to say (Paragraphs 1030 - 1031):

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 - 1445 A.D.) and Trent (1545 - 1563 A.D.). The tradition of the Church, by reference to certain texts of Scripture, speaks of a cleansing fire: (I COR. 3:15, I PET. 1:7)

As for certain lesser faults, we must believe that, before the Final Judgment, there is a purifying fire. He who is truth says that whoever utters blasphemy against the Holy Spirit will be pardoned neither in this age nor in the age to come (MT. 12:31). From this sentence we understand that certain offenses can be forgiven in this age, but certain others in the age to come.