One of the most mis-understood aspects of Catholic theology is that of purgatory. Next to the Eucharist, this is probably the doctrine that most anti-Catholic bigots will condemn as un-Biblical.

Which, I suppose, goes to show the folly of sola scriptura; it's easy to condemn something as un-Biblical when you, personally, are the sole authority by which Scripture is interpreted to you. God forbid you should ever interpret Scripture properly, in light of the teachings and traditions of the Church which has gone before you -- you might just discover that you aren't nearly so correct in your haste to condemn others!

From New Advent (online encyclopedia of all things Catholic):

The Catholic doctrine of purgatory supposes the fact that some die with smaller faults for which there was no true repentance, and also the fact that the temporal penalty due to sin is it times not wholly paid in this life. The proofs for the Catholic position, both in Scripture and in Tradition, are bound up also with the practice of praying for the dead. For why pray for the dead, if there be no belief in the power of prayer to afford solace to those who as yet are excluded from the sight of God? So true is this position that prayers for the dead and the existence of a place of purgation are mentioned in conjunction in the oldest passages of the Fathers, who allege reasons for succouring departed souls. Those who have opposed the doctrine of purgatory have confessed that prayers for the dead would be an unanswerable argument if the modern doctrine of a "particular judgment" had been received in the early ages. But one has only to read the testimonies hereinafter alleged to feel sure that the Fathers speak, in the same breath, of oblations for the dead and a place of purgation; and one has only to consult the evidence found in the catacombs to feel equally sure that the Christian faith there expressed embraced clearly a belief in judgment immediately after death. Wilpert ("Roma Sotteranea," I, 441) thus concludes chapter 21, "Che tale esaudimento", etc.:

Intercession has been made for the soul of the dear one departed and God has heard the prayer, and the soul has passed into a place of light and refreshment." "Surely," Wilpert adds, "such intercession would have no place were there question not of the particular, but of the final judgment.

Some stress too has been laid upon the objection that the ancient Christians had no clear conception of purgatory, and that they thought that the souls departed remained in uncertainty of salvation to the last day; and consequently they prayed that those who had gone before might in the final judgment escape even the everlasting torments of hell. The earliest Christian traditions are clear as to the particular judgment, and clearer still concerning a sharp distinction between purgatory and hell. The passages alledged as referring to relief from hell cannot offset the evidence given below (Bellarmine, "De Purgatorio," lib. II, cap. v). Concerning the famous case of Trajan, which vexed the Doctors of the Middle Ages, see Bellarmine, loc. cit., cap. Viii.

Old Testament

The tradition of the Jews is put forth with precision and clearness in 2 Maccabees. Judas, the commander of the forces of Israel,

making a gathering . . . sent twelve thousand drachmas of silver to Jerusalem for sacrifice to be offered for the sins of the dead, thinking well and religiously concerning the resurrection (For if he had not hoped that they that were slain should rise again, it would have seemed superfluous and vain to pray for the dead). And because he considered that they who had fallen asleep with godliness, had great grace laid up for them. It is therefore a holy and wholesome thought to pray for the dead, that they may be loosed from sins. (2 Maccabees 12:43-46)

At the time of the Maccabees the leaders of the people of God had no hesitation in asserting the efficacy of prayers offered for the dead, in order that those who had departed this life might find pardon for their sins and the hope of eternal resurrection.