First, let’s state what purgatory is not. Purgatory is not a second chance at salvation after death. If a person dies without God's grace, we know of no other chance or opportunity for that person to be saved. Instead, purgatory is for those who die in God's friendship, but have not yet achieved the holiness necessary to enter heaven. In other words, since nothing impure can enter heaven (Revelation 21:27), if we die without being perfectly pure, a purification must happen after death before we can enter heaven. So what things, one may ask, are purified in purgatory?
UNFORGIVEN VENIAL SINS ARE PURIFIED
The Catholic Faith teaches that when a person first comes to Christ, only their past and present sins are forgiven, but not their future sins (those sins that they are yet to commit). For example, in 1st John the apostle John is writing to fellow believers, and he says, "If we confess our sins, he is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness" (1 John 1:9). Now, if all of a believer's future sins are forgiven when they first come to Christ, then there shouldn't be any reason for a believer to have to confess his sins now, since they should already be forgiven. In other words, the only way that this verse would make sense, is if our future sins are not forgiven with when we first come to Christ.
In another place, James, also writing to believers, says in his letter, "Is any one of you sick? He should call the elders of the church to pray over him and anoint him with oil in the name of the Lord. And the prayer offered in faith will make the sick person well; the Lord will raise him up. If he has sinned, he will be forgiven" (James 5:14-15). Notice that James says that if the believer has sinned, he will be (future tense) forgiven. This doesn't make sense if a believer's future sins have already been forgiven when they first come to Christ. Once again, the only way that this verse would make sense, is if only our past and present sins are forgiven when we come to Christ, and not our future sins.
Now, does this mean that every time we sin we lose our hope of salvation? Of course not. Let's go back to John's first letter. In it he also writes, "If anyone sees his brother commit a sin that does not lead to death, he should pray and God will give him life. I refer to those whose sin does not lead to death. There is a sin that leads to death. I am not saying that he should pray about that. All wrongdoing is sin, and there is sin that does not lead to death." (1 John 5:16-17). In these verses, John speaks of two different types of sin. He says that all wrongdoing is sin, but he also says that there is sin that leads to death, and sin that does not lead to death. In other words, there is sin that is mortal and sin that is venial (as the Catholic Church calls them). Mortal sin cuts us off from the presence of God, and creates spiritual death, while venial sin doesn't. Venial sins wound our relationship with God, and many times with those around us, but the normal venial sins that most of us commit everyday do not mean that we lose our hope of salvation.
Now, what if a believer dies while having unconfessed venial sin on his soul? He cannot enter heaven, since nothing impure can enter heaven, but yet, he is not going to hell, since he has the promise of salvation. This is where purgatory comes into the picture. In purgatory, any venial sins that have not been forgiven are purged away.
SINFUL NATURE & ATTACHMENTS TO SIN ARE PURIFIED
Although we have been made new creatures in Christ (2 Corinthians 5:17), we still have a sinful nature that leads us to having attachments to sin. The apostle Paul writes about this in Romans 7:18-19, "I know that nothing good lives in me, that is, in my sinful nature. For I have the desire to do what is good, but I cannot carry it out. For what I do is not the good I want to do; no, the evil I do not want to do—this I keep on doing.”
Even though we have a sinful nature and attachments to sin now in this physical life, we know that we will not have these things in heaven, since nothing impure can enter heaven. This means that between physical death and our entrance into heaven there has to be a purification that purges away our sinful nature and attachments to sin. That purification is purgatory.
ANY UNFULFILLED TEMPORAL PUNISHMENTS ARE FULFILLED
On the cross, Jesus Christ suffered the eternal punishment for our sin, which is separation from God forever in hell, and those who belong to Him are set free from this eternal punishment. But this doesn’t mean that we still do not suffer temporal punishments for our sin. Let me give an example of what I am talking about.
Suppose one of my children disobey me and they do something wrong. They say that they are sorry and I forgive them. But just because I forgive them, that doesn’t mean that they do not have to suffer a punishment. They will either be grounded, have something taken away from them, or be given some other punishment that fits what they did. It is the same with God. Just because God forgives us, there is still a temporal punishment for the wrong that we do. As the writer of Hebrews says, "My son, do not make light of the Lord’s discipline, and do not lose heart when he rebukes you, because the Lord disciplines those he loves, and he punishes everyone he accepts as a son" (Hebrews 12:5-6).
Now, what if a Christian dies with temporal punishment that has yet to be fulfilled? How is it going to be fulfilled before they enter heaven? Once again, this is where purgatory comes into the picture. Any temporal punishment for our sins that remains at the moment of death is fulfilled in purgatory.
CONCLUSION
In conclusion, purgatory is the transition between the sinfulness of this world to the purity of heaven. Through purgatory, the Christian’s remaining venial sins are forgiven, their sinful nature and attachments to sin are removed, and their temporal punishments are fulfilled. They are made completely and perfectly pure and ready to enter heaven.