No. 1478 and 1479, pages 371 and 372 of the Catechism of the Catholic Church: The Celebration of the Christian Mystery; Chapter Two - The Sacraments of Healing; Libreria Editrice Vaticana: Urbi Et Orbi Communications:
An indulgence is obtained through the Church who, by virtue of the power of binding and loosing granted her by Jesus, intervenes in favor of individual Christians and opens for them the treasury of the merits of Christ and the saints to obtain from the Father of mercies the remission of the temporal punishment due for their sins. Thus the Church does not want simply to come to the aid of these Christians, but also to spur them to works of devotion, penance, and charity [cf. Indulgentiarum doctrina, 5].
Since the faithful departed now being purified are also members of the same communion of saints, one way we can help them is to obtain indulgences for them, so that the temporal punishments due for their sins may be remitted.
From the Baltimore Catechism No. 3; Benziger Brothers, Inc. and Tan Books and Publishers, Inc. Nos. 849, 850, 853 and 854, pages 179-180.
Q. How do we show that the Church as the power to grant Indulgences?
A. We show that the Church hs the power to grant Indulgences, because Christ has given it power to remit all guilt without restriction, and if the Church has power, in the Sacrament of Penance, to remit the eternal punishment - which is the greatest - it must have power to remit the temporal or lesser punishment, even outside the Sacrament of Penance.
Q. How de we know that these Indulgences have their effect?
A. We know that these Indulgences have their effect, because the Church, through her councils, declares Indulgences useful, and if they have no effect they would be useless, and the Church would teach error in spite of Christ's promise to guide it.
Q. How does the Church, by means of Indulgences, remit the temporal punishment due to sin?
A. The Church, by means of Indulgences, remits the temporal punishment due to sin by applying to us the merits of Jesus Christ, and the superabundant satisfactions of the Blessed Virgin Mary and of the Saints; which merits and satisfactions are its spiritual treasury.
Q. What do we mean by the "superabundant satisfaction of the Blessed Virgin and the Saints"?
A. By the superabundant satisfaction of the Blessed Virgin and the Saints, we mean all the satisfaction over and above what was necessary to satisfy for their own sins. As their good works were many and their sins few - the Blessed Virgin being sinless - the satisfaction not needed for themselves is kept by the Church in a spiritual treasury to be used for our benefit.