The best way to understand indulgences is to follow their development. The doctrine of indulgences is linked with the doctrine of the communion Saints. The elements of this doctrine are all biblical and were present in the early Church East and West–it is more obvious in the penitential practice of the early Church, but it is still applicable today of course.
First, it bears pointing out that there are three parts to repentance that have been defined by the Church–contrition, confession, and bringing forth fruits worthy of repentance (this last part is often called “satisfaction.”) It is the third part that is related to indulgences. Here are some biblical references to this last part (note: the DRV which I am citing uses the phrase “do penance” or the word “penance” in the place many translations use “repent” and “repentance” but the meaning is the same):
Acts 26:20 But to them first that are at Damascus, and at Jerusalem, and unto all the country of Judea, and to the Gentiles did I preach, that they should do penance, and turn to God, doing works worthy of penance. (see also Matt. 3:8, Luke 3:8 )
Now, there are various ways by which one brings forth fruit worthy of repentance or, in other words, makes satisfaction for sins. This is done through prayer, acts of charity, and self-denial, etc but also suffering through the chastisments that God may send Himself.
Heb. 12:[5] And you have forgotten the consolation, which speaketh to you, as unto children, saying: My son, neglect not the discipline of the Lord; neither be thou wearied whilst thou art rebuked by him. [6] For whom the Lord loveth, he chastiseth; and he scourgeth every son whom he receiveth. [7] Persevere under discipline. God dealeth with you as with his sons; for what son is there, whom the father doth not correct? [8] But if you be without chastisement, whereof all are made partakers, then are you bastards, and not sons. [9] Moreover we have had fathers of our flesh, for instructors, and we reverenced them: shall we not much more obey the Father of spirits, and live? [10] And they indeed for a few days, according to their own pleasure, instructed us: but he, for our profit, that we might receive his sanctification. [11] Now all chastisement for the present indeed seemeth not to bring with it joy, but sorrow: but afterwards it will yield, to them that are exercised by it, the most peaceable fruit of justice.
The Church from the very beginning also prescribed such acts of satisfaction. One common one, early on, was cutting the sinner off from the sacraments for a period of time (this is still common in the East and for certain more serious sins in the West). St. Paul prescribes such satisfaction for the incestuous man in Corinth:
1 Cor. 5:[3] I indeed, absent in body, but present in spirit, have already judged, as though I were present, him that hath so done, [4] In the name of our Lord Jesus Christ, you being gathered together, and my spirit, with the power of our Lord Jesus; [5] To deliver such a one to Satan for the destruction of the flesh, that the spirit may be saved in the day of our Lord Jesus Christ.
Later, the Church adopted other forms of satisfaction in different times and places many taking months or even years to complete. For example, someone who committed a very grievous sin might have to live a strict disciplined life in a monastery for a period of time (this is why prisons are often called penitentiaries, from the root “penitent.”)
If someone were to die before bringing forth worthy fruits, that process was and is understood to be finished in the afterlife as the Council of Florence explained:
Also, if truly penitent people die in the love of God before they have made satisfaction for acts and omissions by worthy fruits of repentance, their souls are cleansed after death by cleansing pains;
An indulgence is a remittance of this need to make satisfaction either partially or fully. St. Paul granted such a pardon to the same incestuous man in Corinth:
2 Cor. 2 :[6] To him who is such a one, this rebuke is sufficient, which is given by many: [7] So that on the contrary, you should rather forgive him and comfort him, lest perhaps such a one be swallowed up with overmuch sorrow. [8] Wherefore, I beseech you, that you would confirm your charity towards him. [9] For to this end also did I write, that I may know the experiment of you, whether you be obedient in all things. [10] And to whom you have pardoned any thing, I also. For, what I have pardoned, if I have pardoned any thing, for your sakes have I done it in the person of Christ.
It should be noted that during certain periods, partial indulgences were delineated by periods of time like days or years to correspond to prevailing penitential disciplines, but today they are generally called “partial” only and their value is relative to the act on which the granting of the indulgence is conditioned.
Anyway, since the need to make satisfaction extends into the afterlife, it followed logically that the indulgence would also.
Matt. 18:18 Amen I say to you, whatsoever you shall bind upon earth, shall be bound also in heaven; and whatsoever you shall loose upon earth, shall be loosed also in heaven.
(see also Matt. 16:18)
Otherwise, if one were loosed on earth, but it did not take effect in the afterlife, the indulgence would be a cruelty deceiving the penitent into thinking he had brought forth sufficient fruits when he had not.
continued…
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Longer than I expected, though. 
