What is purgatory and is it a punishment?

It is a place of purification after death. Let's use prison for an example. When a person commits a crime, he goes to court, and the court finds him guilty of that crime. He says he is sorry and will never do it again, but, still has to "pay the price" for committing that crime, which would be a jail term. When he is released from jail, he goes on to live a good life (hopefully) Some people, if the crime is serious, like murder, are executed. Even though they are sorry that they did it. Suffering is a mystery, and sometimes, mostimes, we cause our own. However, through Jesus dying on the cross, we are able to be forgiven for the sins we commit, even though we still need to do penance (pay for our mistakes). No sin can enter God's kingdom. That is why through God's mercy, we are purified before we enter into God's presence.