Grace and good works affect others not only in natural, but in mystical ways
Reading Exodus 20, the Torah, again:
“…I am the Lord thy God, mighty, jealous, visiting the iniquity of the fathers upon the children, unto the third and fourth generation of them that hate me. And shewing mercy unto thousands to them that love me, and keep my commandments.”
The good we do, by the grace of Christ, ripples out into the universe and builds up His Body:
“If so ye continue in the faith, grounded and settled, and immoveable from the hope of the gospel which you have heard, which is preached in all the creation that is under heaven: whereof I Paul am made a minister. Who now rejoice in my sufferings for you and fill up those things that are wanting of the sufferings of Christ, in my flesh, for His body, which is the church…”
When we cooperate with grace — when we pray, give alms, fast, offer up our sufferings, etc. — we literally strengthen the Body of Christ in a mystical way! Christ Himself and all the Saints of 2,000 years (by the grace of Christ) have built up His Mystical Body (the Catholic Church) and laid up a “treasury of merit” or “spiritual treasury,” as it is also called. In the same way we or others detract from the Body of Christ through sin, we and others add to this treasury — and receive the fruits thereof when we receive an indulgence, for we are one in the Body of Christ:
“We being many, are one body in Christ, and every one, members one of another.”
And read once again I Corinthians 12:26:
“And if one member suffer any thing, all the members suffer with it: or if one member glory, all the members rejoice with it.”
The Church was given the power to bind and loose
To Peter was given the Keys to the Kingdom (Matthew 16) and the power of binding and loosing (forbidding/permitting, condemning/acquitting). In exercising this power of the Keys, the Church has the authority to determine certain practices which help us to to benefit from the treasury of merit and alleviate the temporal effects of sins we’ve confessed and are already forgiven for. This is an indulgence.
That the Church was given the power to forgive the eternal effects of sin through the Sacrament of Penance makes it easier to understand how the Church also has the power to alleviate the lesser, temporal effects of sin. The Church whose priests were given the authority by Christ to forgive the guilt of sin and thereby, by the Blood of Christ, eliminate the eternal punishments for sin, surely also has the authority to pardon the temporal punishments of sin.