A couple of interesting quotes from the interview:
When we pray for the souls, we’ve got to remember we’re giving them paradise, the face of God, when we get them out sooner from purgatory. Our prayers are shortening this horrible suffering of being without God. They then show us their gratitude in the same proportion to their joy.
...we’re given this great power and privilege to release souls from purgatory. Only we are the deliverers. Christ turns to the Church militant. Heaven encourages us. For whatever reason, we’ve been given this great honor and privilege. We’re responsible to pray for our dead.
II Maccabees 12:43-46: "And making a gathering, he [Judas] sent twelve thousand drachmas of silver to Jerusalem for sacrifice to be offered for the sins of the dead, thinking well and religiously concerning the resurrection, (For if he had not hoped that they that were slain should rise again, it would have seemed superfluous and vain to pray for the dead,) And because he considered that they who had fallen asleep with godliness, had great grace laid up for them. It is therefore a holy and wholesome thought to pray for the dead, that they may be loosed from sins."