"Now there is no need to pray for the dead who are in Heaven, for they are in no need; nor again for those who are in Hell, because they cannot be loosed from sins. Therefore after this life, there are some not yet loosed from sins, who can be loosed there from; and the like have charity, without which sins cannot be loosed, for ‘charity covereth all sins’ [Prov. 10:12]. Hence they will not be consigned to everlasting death, since ‘he that liveth and believeth in Me, shall not die for ever’ [Jn. 11:26]: nor will they obtain glory without being cleansed, because nothing unclean shall obtain it, as stated in the last chapter of the Apocalypse (verse 14). Therefore some kind of cleansing remains after this life.
If the debt of punishment is not paid in full after the stain of sin has been washed away by contrition, nor again are venial sins always removed when mortal sins are remitted, and if justice demands that sin be set in order by due punishment, it follows that one who after contrition for his fault and after being absolved, dies before making due satisfaction, is punished after this life. Wherefore those who deny Purgatory speak against the justice of God…”
catscans.com/catholicsite/purgatry.htm
“To understand this doctrine and practice of the Church, it is necessary to understand that sin has a double consequence. Grave sin deprives us of communion with God and therefore makes us incapable of eternal life, the privation of which is called the ‘eternal punishment’ of sin. On the other hand every sin, even venial, entails an unhealthy attachment to creatures, which must be purified either here on earth, or after death in the state called Purgatory. This purification frees one from what is called the ‘temporal punishment’ of sin. These two punishments must not be conceived of as a kind of vengeance inflicted by God from without, but as following from the very nature of sin. A conversion which proceeds from a fervent charity can attain the complete purification of the sinner in such a way that no punishment would remain. [Cf. Council of Trent (1551): DS 1712-1713; (1563): 1820.]”