Today is the day the Church remembers and prays for all the souls of the deceased who are still undergoing purification.
Catholic teaching is that those who die without being fully purified of sin receive that purification in the next life. Purgatory is not a physical place but a state. It's a sign of God's mercy, for he gives us the opportunity to grow in love and cast off the remnants of sin.
The best way to avoid purgatory, of course, is to avoid its cause: sin. Our age seems to have a diminished sense of sin, which may be why teachings like purgatory have fallen out of the popular awareness. In some traditionally Catholic countries, like Italy, however, devotion to the holy souls is very strong. The Italian sisters in my community are very devoted to their souls!
When I saw the movie Gladiator, I noticed that the hero (played by Russell Crowe but I forget the character's name) was a pagan. But he had a great devotion to his deceased ancestors, even to the point of having little statues of them and burning incense and candles. So it must have been a part of the pre-Roman Etruscan culture of Italy, which the Romans also had. When Christianity came, this element of the culture was like a "seed of the gospel" that must have made it easier for the people to understand Christian teachings about the afterlife.