Urquhart provided some good Scriptural references: take a close look at one of them, Matthew 5:26. Prior to this verse, Jesus has just spoken of the need to be reconciled with our brother before we offer our gifts at the altar (notice: it is assumed that we are already part of the body of worshippers–believers–and that we are participating in offering gifts at a public worship…sounds kinda like Mass, eh?). He then goes on to emphasizes the need for reconciliation before coming before the judge (that is, at our death): “Make friends quickly with your accuser, while you are going with him to court, lest your accuser hand you over to the judge, and the judge to the guard, and you be put in prison; truly, I say to you, you will never get out till you have paid the last penny.” Notice that the individual who has not reconciled with all those who may have some grievance against him is NOT sent into everlasting torment (hell), but is sent to a place where he must stay until his debts are paid. The implication is that after he pays the last penny, he will be released. When we pray for the souls in Purgatory, and offer penances for them, we are helping to pay off their debt. Now, some might respond that Jesus paid all of the debt, but that’s not consistent with what is going on here in the story that Jesus tells: if Jesus’ sacrifice had paid this guy’s debt, then why does the Judge (God) not let the guy off entirely?
Jesus describes a similar situation in Matthew 18:23-35. There the king (think God) forgives the debt of a servant who owes him a tremendous amount of money, but the servant then goes off and is unmerciful to a fellow servant who owes him a trifling amount. Look at verse 32: “‘You wicked servant! I forgave you all that debt because you besought me, and should not you had mercy on your fellow servant, as I had mercy on you?’ And in his anger his lord delivered him to the jailers, TILL HE SHOULD PAY ALL HIS DEBT.” Notice: God had already shown his mercy to the servant. The debt had been forgiven—God (Jesus) paid it. Yet because of the servant’s sins (committed AFTER the act of mercy), he is still going to be punished UNTIL he has paid the debt. Presumably, then, once he “pays”, he’s released.
Another useful (and often used) illustration of purgatory is the broken window analogy: say I break my neighbor’s window in a fit of anger. Then, when I come to my senses, I realize how sinful I was and ask my neighbor for forgiveness. Because he is merciful, my neighbor forgives me. But the window is still broken (the effects of sin), and I am expected to pay for it even though my neighbor has entirely forgiven me. Purgatory is how God has us “pay” for the effects of sin (the brokeness of the window). We can pay while we are on earth, but if we have not sufficiently paid for it by the time we die (meaning, that we have made sufficient reparation, including the purification of one’s desires towards breaking windows in the future), we will do so in Purgatory.If we die while still harboring a strong desire to break windows, we will need to “wash up” a bit and rid ourselves of that desire before we sit down to the banquet.
Also, ask your friends what they make of Colossians 1:24: “Now I rejoice in my sufferings for your sake, and in my flesh I complete what is lacking in Christ’s afflictions for the sake of his body, that is, the church…”. Catholics see “what is lacking” is their participation.