This is a reference to the Catholic belief that sin can be atoned for through confession and the acceptance of a self-imposed punishment, called a penance. This atones for the sin, and wipes away some of the time the sinner will have to spend waiting to enter heaven.
Even in the early days of Christianity, this concept proved problematic. Acts of penance tend to involve privations such as fasting, self-flagellation or undertaking pilgrimage. They thus have little to do with the actual sin committed, which means a person can absolve themselves of a sin without taking any personal responsibility for the results of that sin. For example, if you steal something and commit penance, why do you then have to accept an earthly punishment for your crime, seeing as God trumps any earthy authority who tries to hold you to account?
It's an interesting choice for Pullman to highlight, because penance became one of the most-hated aspects of the Catholic church during the middle ages. It began to sell Indulgences, which were essentially automatic forgiveness of sins in exchange for money. The idea the rich could almost literally buy their way into heaven was widely seen as unjust. To make matters worse they Church employed Pardoners, individuals who went out and aggressively sold Indulgences, often with the aim of raising money for specific church projects. This was a direct contributor to the Protestant reformation, as Martin Luther decided to write his famous Ninety-Five Theses after hearing his parishioners say they no longer needed to change their sinful behavior after purchasing Indulgences.
"Preemptive" penance has never been official dogma, and indeed it does not stand up to logical scrutiny. If one wishes to obtain forgiveness of a sin in advance, one clearly has the intention of sinning and, therefore, cannot truly be repentant. However, it's a clever way of both setting up a plot point and highlighting the inherent problems in the very concept of penance, especially the one of personal responsibility. And it's very close indeed to the idea of Indulgences which, in Britain at least, are widely learned about at school and understood as an unfair abuse of power on the part of the church.
This is, then, a key plank in a central theme of the trilogy, which is the inherent oppression that results when organised religion rigidly applies doctrine and dogma. Preemptive absolution is not merely unfair: it is illogical and is deliberately used as a tool of subjugation. That it is secret - not widely known outside the church - speaks volumes about the inherent hypocrisy of a supposedly benevolent organisation trying to protect its wealth and power. Dogma, Pullman is saying, will always lead to corruption.
So to answer your specific questions:
1. Yes, it is a reference to a real-life doctrine, although no specific parallel exists and it is not directly compatible with actual Christianity.
2. That it is a corrupt and hypocritical organisation as a result of its strict adherence to dogma.