What is purgatory? how is this title appropriate to the play?​

I’m not sure what play you’re talking about but purgatory is the catholic (and maybe some other religions) belief that before entering heaven or hell, you wait in purgatory. It is a middle ground, often thought of for waiting. If you paid the church (I can’t remember what their payments are called) then you could skip purgatory and go to heaven. This is one of the things that caused the church to have different denominations.