Why Pray For The Dead

When a soul reaches purgatory, it can no longer pray for themselves. When we offer masses, prayers, sacrifices, works for the Holy Souls it shortens their time in purgatory.

The Catechism of the Catholic Church states:

1032 This teaching is also based on the practice of prayer for the dead, already mentioned in Sacred Scripture: "Therefore Judas Maccabeus] made atonement for the dead that they might be delivered from their sin." 609 From the beginning the Church has honored the memory of the dead and offered prayers in suffrage for them, above all the Eucharistic sacrifice, so that, thus purified, they may attain the beatific vision of God. 610 The Church also commends almsgiving, indulgences, and works of penance undertaken on behalf of the dead:
Let us help and commemorate them. If Job's sons were purified by their father's sacrifice, why would we doubt that our offerings for the dead bring them some consolation? Let us not hesitate to help those who have died and to offer our prayers for them. 611

2 MACCABEES 12:38:45

38 Then Judas assembled his army and went to the city of Adullam. As the seventh day was coming on, they purified themselves according to the custom, and they kept the Sabbath there. 39 On the next day, as by that time it had become necessary, Judas and his men went to take up the bodies of the fallen and to bring them back to lie with their kinsmen in the sepulchres of their fathers. 40 Then under the tunic of every one of the dead they found sacred tokens of the idols of Jamnia, which the law forbids the Jews to wear. And it became clear to all that this was why these men had fallen. 41 So they all blessed the ways of the Lord, the righteous Judge, who reveals the things that are hidden; 42 and they turned to prayer, beseeching that the sin which had been committed might be wholly blotted out. And the noble Judas exhorted the people to keep themselves free from sin, for they had seen with their own eyes what had happened because of the sin of those who had fallen. 43 He also took up a collection, man by man, to the amount of two thousand drachmas of silver, and sent it to Jerusalem to provide for a sin offering. In doing this he acted very well and honorably, taking account of the resurrection. 44 For if he were not expecting that those who had fallen would rise again, it would have been superfluous and foolish to pray for the dead. 45 But if he was looking to the splendid reward that is laid up for those who fall asleep in godliness, it was a holy and pious thought. Therefore, he made atonement for the dead that they might be delivered from their sin.
SIRACH 7:33

33 Give graciously to all the living and withhold not kindness from the dead.