Purgatory is a doctrine that's been ridiculed by Protestants and almost totally forgotten by many Catholics. With the erroneous idea that "all men are saved" being held by many Catholics, people don't think their loved ones — if they even died in the state of grace — may be suffering in Purgatory.
There are three sure things in every one of our lives: death, judgment, Heaven or Hell. Theologians call this the "eschaton" — the last things. We will all die, be judged by God on our actions, and go either to Heaven or to Hell, depending on how we lived our lives on earth.
Those who die with even one mortal sin unrepented of on their souls will forever reside in Hell with Lucifer and the other reprobate souls. Their sentence will be final and irrevocable.
Those who die in the state of grace, with the presence of the Holy Trinity in their souls, will not be condemned to eternal suffering, but in order for them to attain Heaven they must be perfect, with no stain of sin on their souls. Our Lord said, "You therefore are to be perfect, even as your heavenly Father is perfect" (Matt. 5:48).
A soul is like a window. When we sin we're like the boy who throws a rock through the window, breaking the glass. In shame and sorrow, the boy goes to his father, confesses his transgression and obtains his father's forgiveness, but the window must still be repaired — the glass is still broken. The boy will have to do extra work around the neighborhood on top of his regular chores around the house to make enough money to buy a new piece of glass and fully repair the window.
The souls in Purgatory are like this. They lived virtuous lives on earth but they didn't atone for all their sins before they died. This will probably be the case for most people who die in the state of grace.
These souls are popularly referred to as the Poor Souls in Purgatory, and they are in a state of suffering that we can't comprehend here on earth. They suffer according to the sins for which they are atoning.
In a pious account, a poor soul communicated to a friend he would rather suffer everything the earth had to offer for a thousand years rather than a second of Purgatory. Yet with all that suffering, those souls aren't able to offer any of it for themselves — but they can offer prayers on behalf of others.
Their time and amount of suffering can be shortened or lessened only by our prayers. November 2 is the date the Church has traditionally celebrated as the feast of All Souls. It is a day for Catholics to remember the suffering souls in Purgatory. Scripture says, "It is therefore a holy and wholesome thought to pray for the dead, that they may be loosed from sins" (2 Mac. 12:46). The Church also especially designates the month of November to the Holy Souls so that the faithful might especially pray and atone for the sufferings of our brothers and sisters in Purgatory.
Saints have revealed that our sufferings on earth are worth more for us and others than if we were to suffer for them in Purgatory. The souls in Purgatory can pray for us as well, and when their purification is complete, they go to Heaven and pray for those who helped to set them free.