Many of the other answers here describe purgatory accurately as, historically, a Catholic idea of a place where one who can be made worthy of salvation is made pure and worthy of heaven.
Let's take a wider look at the notion. "Purgatory" is related to "purge." We all know that none of us lives a perfect life, and some live better lives than others. So how can there be a simple "some go to heaven, and others go to hell"? This is a very troubling idea.
Those who believe in reincarnation can answer this in terms of more lifetimes ahead, where we learn more and more, and become purer and purer.
But mainstream Christianity, early on, rejected the idea of reincarnation. Yet "heaven or hell at the end of one life" is a very uncomfortable idea. Purgatory was developed as a solution.
I suggest that, instead of thinking about where we go after the body dies, we live now, breath by breath, moment by moment, as purely and lovingly as we can. Love all life, and let what happens, happen!