Purgatory is the state in which those suffer for a time who die guilty of venial sins, or, without having satisfied for the punishment due to their sins. After the general judgment there will be Heaven and Hell, but no Purgatory, for there will be no men living or dying upon the earth in its present condition to go there. All will be dead and judged and sent to their final abodes.

Those in Purgatory are the friends of God; and knowing Him as they so now, they would not go into His holy presence with the slightest stain upon their souls; still they are anxious for their Purgatory to be ended that they may be with God. They suffer, we are told, the same pains of sense as the damned; but they suffer willingly, for they know that it is making them more pleasing to God, and that one day it will all be over and He will receive them into Heaven. Their salvation is sure, and that thought makes them happy. If therefore, you believe that any of your family or friends are in Purgatory, you should help them all you can, and try by your prayers and good works to shorten their time of suffering.

They will help you (though they cannot help themselves) by their prayers. And oh, when they are admitted into Heaven, how they will pray  for those that have helped them out of Purgatory! If you do this great charity, God will, when you die, put in some good person's heart to pray for you while you suffer in Purgatory. There must be a Purgatory, for one who dies with the slightest stain of sin upon his soul cannot enter Heaven, and yet God would not send him to Hell for so small a sin.

But why does God punish those He loves? Why does He not forgive everything? He punishes because He is infinitely just and true. He warned them that if they did certain things they would be punished; and they did them, and God must keep His promise. Moreover He is just, and must give to everyone exactly what he deserves.

Baltimore Catechism No. 4