See also The Treatise on Purgatory by St Catherine of Genoa at Amazon.
Punishment, like a shadow, the Fathers teach, follows all sin, whether mortal or venial, and it is not usually remitted to the full when forgiveness is obtained. Eternal punishment, incurred by mortal sin, is always remitted with the guilt, but some temporal punishment generally remains due to the justice of God.
This temporal punishment is inflicted by God either in this life or in Purgatory; but a man may anticipate the divine justice by works of penance, or by means of Indulgences.
The guilt, then, of sin is one thing, the punishment another. The guilt is remitted when a man truly repents, either with or without the Sacrament of Penance; but though the punishment, or a portion of it, may be remitted with the guilt, some usually remains, as a debt of satisfaction, to be paid in this world or the next.

This truth is clearly indicated in the sacramental penances which always accompany Absolution. These penances have, in course of time, under pressure of external circumstances, lost much of the severity which characterized them in earlier ages, but they still testify to the principle that after forgiveness satisfaction remains due.
The comparative lightness of modern sacramental penances ought to suggest that they alone are not sufficient to satisfy the justice of God, and that they should be supplemented either by other penances, self-inflicted or patiently accepted at the hand of Goc, or by some equivalent. And in the case of sins forgiven either indirectly in the Sacrament, or by means of contrition alone, the satisfaction remaining due is left altogether to the individual’s patience under chastisement from God, or to his personal activity in applying himself either to works of penance, or to some equivalent.
That equivalent is to be found in Indulgences. What, then, is an Indulgence? An Indulgence is the remission by the Church, on specified conditions, of the whole or a part of the debt of satisfaction remaining due for sin. The Church has power to absolve from guilt; she has also power to remit the punishment. The one she exercises in the Sacrament of Penance; the other she exercises when she grants an Indulgence. And it is clear from what has been said that an Indulgence is supplemental to Absolution, and presupposes the forgiveness of the guilt of sin.
Theologically considered, an Indulgence is not a mere exercise of spiritual power and authority on the part of the Church ; it is truly a payment of the debt, made out of her Treasury of satisfactory merit; for in this are stored up the superabundant merits of JESUS CHRIST, and the accumulated merits of our Lady and all the Saints. With this inexhaustible fund at her command, she has the means of satisfying the debts due from her children to the justice of GOD.
In form, an Indulgence emanates from the Pope; leaving out of account the limited power exercised by Bishops in favour of their flocks and by Cardinals, Nuncios and others; and it is registered in a Decree or Rescript of the Congregation of Indulgences, or some similar document. It attaches to a specified prayer or good work an additional satisfactory value, such value being expressed in the terms of an ancient canonical penance, viz., so many days, Quarantines (which lasted forty days), or years, to which the Indulgence is there by declared to be equivalent.

The earliest Indulgences were, in fact, remissions of these very penances. Indulgences are either Plenary or Partial, according as a remission of all, or of part, of the debt of punishment due is granted. In either case the actual benefit obtained depends upon the dispositions of the penitent, and the care and accuracy he employs in fulfilling the conditions laid down. For the sake of clearness and facility of reference, the general and special conditions required for obtaining Indulgences are set out in tabular form below.
It only remains to add that, though the Church has no direct jurisdiction over the souls in Purgatory, she authorizes and encourages, as a work of supreme charity, the application of Indulgences, by way of suffrage, to the needs of those afflicted souls; and we may confidently assure ourselves that these suffrages are most acceptable to the Divine Majesty, and that what the Church would thus, as it were, indirectly loose in Purgatory is speedily loosed also in Heaven, amid the rejoicing of all the heavenly court, to the great glory of GOD, and to the incalculable benefit, as well of the suffering souls as of their earthly benefactors.
General Conditions required for all Indulgences.
1. STATE OF GRACE.
2. INTENTION. (See Decisions 3, 4,)
3. ACCURACY and DEVOTION in fulfilling the specified conditions. (See N.B. ibid.)
Special Conditions usually required for Plenary, and sometimes for Partial, Indulgences.
i. CONFESSION.
ii. COMMUNION.
iii. VISIT to a church or public chapel. (See p, xiii.) iv.
PRAYER according to the intention of the Pope. (See p. xiii.)
N.B. Too much stress cannot be laid on the importance of carefully noting and exactly fulfilling all that may be required for gaining a particular Indulgence.
Source: The Raccolta (1910)
