Thanks Katzpur this ought to be a good discussion. I will first try to define purgatory as best I can and then I shall explain my definition, then perhaps you can compare it to the concept of the spirit world or just define it on its own, whatever works.
Purgatory is the process by which the temporal effects of sins, that have had their eternal effects wiped away, are purged from the sinner before entering into the fullness of heaven.
This may not be the best definition so here is one I picked up off a good Catholic website
Purgatory: a place or condition of temporal punishment for those who, departing this life in God's grace, are, not entirely free from venial faults, or have not fully paid the satisfaction due to their transgressions.
I was talking with my spiritual director today and he said an interesting thing. He said (and I paraphrase) We have already achieved heaven by way of Jesus. We are not trying to get to heaven in this life, we are trying to avoid hell. I think this is a very positive way to look at it, we are not trying to get to heaven as much as we are simply trying not to lose it. And I believe, I hope and pray, that most if not all peoples will be able to avoid hell. After one dies there is only two places to go, heaven or hell.. So those who have avoided hell must be going to heaven. Yet one must be perfect in order to enter fully into heaven (So be perfect, just as your heavenly Father is perfect. Matthew 5:48). Purgatory then, is the stage of heaven which those who have been saved are cleaned up, if you will, before they enter fully into heaven.
So the key point here, I think, is that we believe that sin has both a temporal and eternal consequence. The eternal consequence of any sin is eternal death, separation from God, basically hell. That means any little tiny sin has the eternal consequence of eternal damnation. Thankfully God became man in Jesus the Christ and in His incarnation, passion, death, and resurrection, He paid the eternal price for our sins. Now even the most egregious sin can have its eternal consequence wiped away by the blood of Christ, our sins have been paid for and hell can be avoided by everyone through Gods mercy and forgiveness by the work of Jesus. Sweet!
This is not the end of it, However. Our sins still have a temporal consequence. So even after ones sins have been forgiven one must make satisfaction or do penance to remove the temporal stain of sin. Now if you think about it for a second this seems to make sense. When we do sinful things it affects our lives and the lives of those around us, especially those habitual sins that one can easily fall into, like when a person becomes an alcoholic, for example. One can be forgiven for drinking too much but this does not mean that the road to sobriety will be any easy one. That person must go through all kinds of difficulty in avoiding alcohol, they have to reconcile with those peoples that they estranged through their habit, etc. So this idea of a temporal effect of sin makes allot of practical sense. Our behavior, even if it has been forgive by God, still effects our lives and who we are and how we deal with others. This is what purgatory is all about. If one dies in the grace of God then the eternal consequence of hell is avoided but there may still remain in a person the effects of all their sins. And, generally speaking most people fall into this category when they die, I believe. Purgatory wipes those effects away so that one can be made perfect and enter into heaven.
So that looks like a good start to me.