From what I understand, yes, sort of. It’s a state of being of the soul. In Hell the soul is completely cut off from God, the most painful existence of the soul. Heaven is the complete union of the soul with God. Purgatory is the purging process of the soul before entering heaven. The Catholic Church teaches that sin, even after we have sought God’s forgiveness, leaves marks on our soul, much like nails in a piece of wood once you remove them. Purgatory is for heaven-bound souls that need a purging of those marks from sin.

Are they physical places? No one can really prove that (or disprove it). The Scriptures are known for depicting things with vivid imagery not so much as to describe the exact details of such a thing, but to give the reader, us, an analogy so we can understand its significance.