In the communion of saints, "a perennial link of charity exists between the faithful who have already reached their heavenly home, those who are expiating their sins in purgatory and those who are still pilgrims on earth. between them there is, too, an abundant exchange of all good things." In this wonderful exchange, the holiness of one profits others, well beyond the harm that the sin of one could cause others. Thus recourse to the communion of saints lets the contrite sinner be more promptly and efficaciously purified of the punishments for sin. CCC 1475
In today's reading, the Catechism discusses the purposes of indulgences. To be honest, this is one doctrine that I've struggled with the most. Perhaps this comes from my years as a Protestant, but it's not been easy to fully wrap my head around. Intellectually, sure I understand the basic concept. The Catechism Compendium gives a decent enough summary:
Indulgences are the remission before God of the temporal punishment due to sins whose guilt has already been forgiven. The faithful Christian who is duly disposed gains the indulgence under prescribed conditions for either himself or the departed. Indulgences are granted through the ministry of the Church which, as the dispenser of the grace of redemption, distributes the treasury of the merits of Christ and the Saints. (#312)
I get that they are bound with the Church's "binding and loosing" authority granted by Christ (Matt 16:19; 18:18). The Eastern Orthodox too had something akin to this for a few centuries. Certainly the "prayers and good works" of the Blessed Theotokos and Christ's holy saints are "truly immense, unfathomable, and even pristine in their value before God" (CCC 1477). Yet I must confess, this is something which I largely accept on faith because I do believe the Church was founded by Jesus Christ. My puny brain has trouble understanding it all. There is a book that's been recommended to me, which I've been meaning to get: Indulgences: Luther, Catholicism, and the Imputation of Merit. Perhaps that's a good resource to help resolve any confusion. I'll have to revisit this subject at a later time.
The Catechism Companion, Vol II has some pretty good commentary on this:
Some people have concerns about indulgences because they seem like buying grace, but purchasing spiritual goods is absolutely prohibited by the Church and Scripture. Indulgences involve letting go of attachments to earthly things and growing in our relationship with the Lord. The Church believes in growing in holiness and cooperating with God's grace. God has given us his grace, but we must work with it to grow spiritually. (p. 170)
Purgatory, by Peter Paul Rubens
This image of purgatory remind us that the souls there are part of the communion of saints, and thus our prayers and sacrifices can help remit their temporal punishment (see CCC 1479). (p. 171)