Purgatory
Yes, the Church teaches that Purgatory exists. Here is an explanation I have heard.
God is perfect holiness
Is 6:3 And one called to another and said: "Holy, holy, holy is the LORD of hosts; the whole earth is full of his glory."
Rev 4: 8 And the four living creatures, each of them with six wings, are full of eyes all round and within, and day and night they never cease to sing, "Holy, holy, holy, is the Lord God Almighty, who was and is and is to come!"
We are called to that same holiness
Mt 5:48 You, therefore, must be perfect, as your heavenly Father is perfect.
I Peter 1:15 but as he who called you is holy, be holy yourselves in all your conduct; 16 since it is written, "You shall be holy, for I am holy."
Without perfect holiness, we cannot see God in heaven.
Heb 12:14 14 Strive for peace with all men, and for the holiness without which no one will see the Lord.
Rev 21: 27 But nothing unclean shall enter it, nor any one who practices abomination or falsehood, but only those who are written in the Lamb's book of life.
So, 1) God is perfect holiness, 2) we are called to that holiness, 3) nothing unholy can enter heaven, 4) we are not perfectly holy now, and 5) we know by faith that we will enter heaven….. So something must happen to us between now (when we are un-holy in our experience since we do sin) and then ( when we will be perfectly holy in fact and in our experience), and that something is a process that takes us where we are now and makes us perfect when we get to heaven. That process starts now, and ends when it is complete when we enter Gods throne room in heaven. That process is called purgatory.
I personally think its best to let this purification progress as much as possible now in this life. Its better for me, since if I allow God to purify me, I can love and serve Him better. Its better for you and the church since if I am loving and serving Him better, you have a better witness of His grace and can more easily come close to God yourself.
Here is another place to begin: do you think that when each of us gets to heaven, that you will see how much more you could have done for God if you had been more faithful? Do you think that with the heavenly vision, you will see how your failures were an obstacle to keep someone else from coming more fully or more quickly to Christ? I think that with the heavenly clarity we will receive at that time, that we will see this and feel this way. But do you think that this state of remorse for earthly shortcomings and failures will endure for ever? No, this state of regret will be washed away as we enter fully into heaven, there to be in God’s very throne room to praise and worship Him in fullness. This state of regret is temporary. This temporary state of regret for sin and failure is what Catholic theology calls Purgatory. Why does He say, speaking of eternity in Rev 21:4 “ He will wipe away every tear from their eyes” unless there are tears to be wiped away?
Other thoughts:
Purge meaning “to purify or cleanse” Purgatory: an intermediate state of purification.
Only imperfect saints in the state of grace enter Purgatory.
Purgatory exists for purification and reparation. The effects of sin are purged. The stain of sin is removed.
Purgatory is only temporary. Everyone in Purgatory will go to heaven.
After everyone experiencing Purgatory is done with it and gone on to heaven, Purgatory will cease to exist.
Where is the doctrine of purgatory referred to in the Bible?
Mt 12:32 “And whoever says a word against the Son of man will be forgiven; but whoever speaks against the Holy Spirit will not be forgiven, either in this age or in the age to come.” (Are there sins that can be forgiven, that can be dealt with, in the age to come?)
I Cor 3:15 If any man's work is burned up, he will suffer loss, though he himself will be saved, but only as through fire.
I Peter 3:18 For Christ also died for sins once for all, the righteous for the unrighteous, that he might bring us to God, being put to death in the flesh but made alive in the spirit; 19 in which he went and preached to the spirits in prison, 20 who formerly did not obey, when God's patience waited in the days of Noah, during the building of the ark, in which a few, that is, eight persons, were saved through water.
I Peter 4:6 For this is why the gospel was preached even to the dead, that though judged in the flesh like men, they might live in the spirit like God.” (Note that it is a prison for disobedient spirits, and they were saved when Jesus preached to them. This is not hell, because no one is saved from hell. This is not heaven, because there are no disobedient spirits there. St. Peter is describing a temporary state for disobedient souls who were eventually delivered from this state by Jesus. )
2 Maccabees 12: 44 For if he were not expecting that those who had fallen would rise again, it would have been superfluous and foolish to pray for the dead. 45 But if he was looking to the splendid reward that is laid up for those who fall asleep in godliness, it was a holy and pious thought. Therefore he made atonement for the dead, that they might be delivered from their sin.
Here is the complete discussion of what Purgatory is, from the Catechism of the Catholic (CCC) Church: If you want to see the foot notes, check on http://www.scborromeo.org/index2.htm )
Note that the CCC does not refer to it as a time or a place, but simply as a “state.”
III. THE FINAL PURIFICATION, OR PURGATORY
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.606 The Church formulated her doctrine of faith on Purgatory especially at the Councils of Florence and Trent. The tradition of the Church, by reference to certain texts of Scripture, speaks of a cleansing fire:607
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. From this sentence we understand that certain offenses can be forgiven in this age, but certain others in the age to come.608
1032 This teaching is also based on the practice of prayer for the dead, already mentioned in Sacred Scripture: "Therefore [Judas Maccabeus] made atonement for the dead, that they might be delivered from their sin."609 From the beginning the Church has honored the memory of the dead and offered prayers in suffrage for them, above all the Eucharistic sacrifice, so that, thus purified, they may attain the beatific vision of God.610 The Church also commends almsgiving, indulgences, and works of penance undertaken on behalf of the dead:
Let us help and commemorate them. If Job's sons were purified by their father's sacrifice, why would we doubt that our offerings for the dead bring them some consolation? Let us not hesitate to help those who have died and to offer our prayers for them.611