Purgatory is perhaps one of the most misunderstood Catholic doctrine. So much so that even many Catholics have difficulty understanding it. Protestants will err in saying that it's a sort of waiting room before a soul enters Heaven, and Eastern Orthodox will err in saying that Catholics believe it's a light version of Hell. Both of these, however, miss the target, despite the true meaning being in the name itself: purging or purification.
"All who die in God's grace and friendship, but still imperfectly purified, are indeed assured of their eternal salvation; but after death they undergo purification, so as to achieve the holiness necessary to enter the joy of heaven. The Church gives the name Purgatory to this final purification of the elect, which is entirely different from the punishment of the damned."
- Catechism of the Catholic Church § 1030-1031
Even so, the concept of Purgatory can still be difficult to understand: if God has forgiven me of my sins, why must I go through a process of purification? I believe this difficulty with the concept of Purgatory is the product of something I've mentioned in my previous post about Sin & Hell. Although "[Sin] is an offense against God"[1], it would seem we're sometimes limited to believing it is only this, when in reality sin has a real negative effect on our immortal souls, causing deformities to the image & likeness of God in which we were all created. This is similar to how when a child misbehaves: although the child suffers first-hand the consequences of his actions, his bad behaviour is an offense to his father who raised him better. As such, if sin causes injury to our souls, then our souls will also require healing, not just forgiveness of our Heavenly Father. As such, Purgatory is not simply a tiny hell, as it's not a question of punishment.
Yet, sometimes the process for healing and purification can be more painful than the injury itself. Hence why Purgatory is not a waiting room, but rather a place where those who find themselves there are cured back to that perfect image & likeness which they were created with. This process can be painful. To give an analogous anecdote, recently I had cut my hand with a knife; the injury itself hardly hurt, but the process of cleaning it and mending it hurt many times more than the injury itself. If this is true for physical wounds, why would it not be true for wounds of the soul? Our souls require healing and purification.
Catechism of the Catholic Church § 1871