Is Purgatory a part of Divine Revelation?
Yes.
Jesus alludes to its existence in the Gospels (see e.g. Matt 12:32) and his audience knew what he was talking about.
2 Maccabees shows, for example, that the Jews already believed that some souls could die with sins on their conscience that could yet still possibly be forgiven by offering sacrifices to God. Jesus affirms this belief when he teaches that there is a certain sin (the sin against the Holy Spirit) that cannot be forgiven through such expiatory sacrifices known to the Jews which were made by them on behalf of the dead or for the souls of sinners after death (“forgiveness…in…the world to come” (Matt 12:32)).
The Church teaches in the Catechism that the aforesaid sin is the sin of final impenitence or an absolute refusal to acknowledge, cooperate with and accept God’s mercy and grace: it is in effect an ardent or obstinate refusal to be reconciled with God.
The early Christians all prayed for the dead. Again, this would be a futile, worthless and possibly even heretical practice if there simply was no way to console or provide assistance for the dearly departed: they would be either absolutely in heaven or hell for all eternity and entertaining any hope for them would be a violation of God’s just decree. However, if there does exist a “place” where souls are undergoing purification from sin -and this is God’s will- then it is not impious to hope that some souls have gone to that “place”.
Consequently, we can pray to God to have mercy on them or do penitential works (or works of charity) on their behalf to make up for whatever may be lacking on their part:
Colossians 1:
[24] Even as I write, I am glad of my sufferings
on your behalf, as, in this mortal frame of mine,
I help to pay off the debt which the afflictions of Christ still leave to be paid, for the sake of his body, the Church.
Jesus also alludes to a place of punishment for debtors (which is also a temporary one) in the Gospels:
Matthew 5:
[25] If any man has a claim against thee, come to terms there and then, while thou art walking in the road with him; or else it may be that the claimant will hand thee over to the judge, and the judge to the officer, and so thou wilt be cast into prison.
[26] Believe me, thou shalt not be set at liberty until thou hast paid the last farthing.
Notice that you can be released from this “prison” (v.25); that is, you can “be set at liberty” (v.26) but not, however, until you have “paid the last farthing” (v.26, “farthing,” i.e., the last penny as in the old debtor’s prisons where people had to repay your debt to get you released).
When Christians pray for the dead or do works of charity on their behalf, we are attempting to pay those pennies (“farthings”: i.e. their debt):
Matthew 25:
[43] I was a stranger, and you did not bring me home… I was sick and in prison, and you did not care for me.
[44] Whereupon they, in their turn, will answer, Lord, when was it that we saw thee… in prison, and did not minister to thee?
[45] And he will answer them, Believe me, when you refused it to one of the least of my brethren here, you refused it to me.
Purgatory, then, is a kind of debtor’s prison, which is why it is important to pay that debt so those prisoners -who are our and the Lord’s brothers- may be released.
Hebrews 13:
[3] Remember those who are in prison, as if you were prisoners too; those who endure suffering, since you have mortal bodies of your own.