Confession and indulgences tend to get a little mixed up in people's minds, so hopefully this will clarify things a bit.

The sacrament of confession in the Catholic Church is the process by which a church member repents of committed sins (there are two types of sins, by the way: mortal sins, which threaten the sinner with damnation if not repented before death, and venial sins, which are a "lesser" level of sin that does not necessarily threaten damnation). So someone seeking confession who has committed a mortal sin needs to express contrition, ie be truly sorry for committing the sin, and promise to sin no more. As a side note, this is more or less where the Reformation came from, as Martin Luther was very anxious about the eternal well-being of his soul, to the point of questioning how we can ever really know if we are truly sorry, as opposed to just fearing damnation. But that's a whole separate story. Anyway, by expressing contrition and seeking God's forgiveness, the person seeking confession is restored to their relationship with God and spared eternal damnation.

But here's where indulgences come in. Just because that person has confessed their sins, it doesn't mean that were they do immediately drop dead, they would go straight to Heaven. That pretty much is reserved for the saintly and pure. The idea in Medieval Christian thought was that very, very few Christians had that as an option after death, and that most souls, in the words of Kevin Madigan, had a "supernatural debt" that had to be paid off for the committing of sins before a soul could reach the Kingdom of Heaven. In short, the soul needed to be "cleansed" of sin first, in Purgatory (which means "Cleansing" - it did what the name on the tin said). So the vast majority of people who were neither the most wicked nor the most saintly were expected to go through this process.

One means of paying down this "debt" was through the chanting of masses for deceased souls, and this was a major reason for Medieval nobility (who were in the business of often violently killing people) left donations for the founding of monasteries and chapels to say masses for their souls after death - the donor had already sought confession and was therefore forgiven of his/her sins (and therefore spared eternal Hell), but still had to "work off" the sins in Purgatory, and the masses chanted were supposed to shorten that process. Another means for working off the debt was to go on a Crusade, with a Church guarantee that "whoever begins and completes so holy a journey with devotion or dies on it will obtain absolution from all his sins which he has confessed with a contrite and humble heart and he will receive the fruit of eternal reward from him who repays all." Note that a Crusader first must confess and be truly sorry for his sins before using the Crusade to avoid Purgatory.

Just what Purgatory was was something argued by theological theologians, and often theologians were playing catch-up to popular beliefs developing around a third alternative to Heaven and Hell. Pope Gregory the Great wrote of a cleansing process in "certain mansions", but for centuries thereafter there was debate as to the type, duration and intensity of the suffering that a soul would need to experience in Purgatory in order to cleanse it of sin. The general consensus arose though that it did involve suffering, and that the suffering experienced there for even the most venial sins was more painful than the worst pains experienced physically on Earth. It was around 1170 or so among theologians in Paris that Purgatory as a specific place rather than an unspecific "cleansing fire" began to be talked about.

Dante wrote his literary interpretation of Purgatory in the Purgatorio (ie, Divine Comedy Part II), in which he depicts Purgatory as a mountain on the opposite end of the globe from Jerusalem, which souls must climb and pass through trials (such as carrying massive boulders and massing through fires) in order to be cleansed. Personally, this version of Purgatory sounds an awful lot to me like a Crossfit or Ironman program - it's really painful but the people doing it are super into it and are very much focused on the end result goal.

You may see a parallel in financial debts, especially with Madigan's literal connection to "debt". Just because you pay off the principal (ie, you're forgiven of the sin) still means that you also have to pay back the "interest" (ie, time in Purgatory). Social concern over Purgatory especially increased around the time of the Black Death - with many people suddenly facing the possibility of a quick and unforeseen death, there was a concern over the length of time that a soul would then have to spend in Purgatory working off its "debt". This period also saw much greater detail placed on describing in gruesome detail the suffering that souls would experience in Purgatory, and much more explicit detail on the length of time spent there, stretching into the tens of thousands of years.

Of course, if Purgatory can be quantified in terms of years, and if sin can be treated as a "supernatural debt", one means of which is to give donations (such as for the saying of masses for deceased souls), then it almost seems like the logical conclusion that Papal Indulgences would develop: ie, such and such an indulgence was worth taking off such and such number of years in Purgatory. Note that this is not offering forgiveness for sins - only God's forgiveness sought earnestly through the Sacrament of Confession could provide that. This is part of the atonement for sins.

It's worth noting that the idea of Purgatory was not universally accepted during the Medieval period, and was explicitly rejected by a number of heretical groups, such as the Waldensians and many of the Hussites. Clearly, the establishment of chantries to pray for deceased souls, combined with indulgences, the veneration of Saints was big business for the church, and kept many, many monks and priests employed.

But for certain reformers, Luther included, the major issues with these practices that led to the rejection of Purgatory were as much with the lack of Biblical authority for such practices and beliefs, the perceived limitation of God's grace, and the psychological burden placed on the Penitent as with perceived institutional corruption.