What does the Catholic Church teach about purgatory?

For the venial sins you commit on earth, not mortal sins, you are required under a kind of judicial law to give an account, and you can do that here on earth or in purgatory, but they will be accounted for. This is fair, because in this way nobody gets off scot-free; the little sins someone commits against you out of jealousy may not be mortal, but they are sins, and they will be paid for here or in purgatory. Once that punishment is taken care of, the soul is free to go to heaven. The other thing purgatory is for is purifying, which is simultaneous with the punishment; in punishing the soul for its misdeeds, God is in a sense purifying it and preparing it for heaven, because as Revelation 21 says, nothing impure will enter the kingdom of heaven. If we still have venial sin on our soul that has not been adjudicated by indulgences from the Church or by good works, it will be accounted for, and rightly so, because God is fair, and at the same time we are purified. The more the sins are adjudicated and punished, the purer we become, like dross drawn out of gold in the fire, as 1 Corinthians 3 puts it, until we are pure enough to enter the kingdom of heaven. That is what purgatory is.