What is an indulgence?
Indulgence is a remission in whole, or in part, of the temporal punishment due to sin. It is not permission to commit a sin, nor is it forgiveness of the sin itself. A sin can only be forgiven in Confession.
Although an indulgence can grant relief here on earth, it is usually thought of in terms of the afterlife. When we die, unless our soul is in a state of perfect grace, we will most likely go to Purgatory before entering heaven. There our souls will be cleansed and readied to enter into God's presence. Simply put, indulgences give us some time off for good behavior.
http://www.newadvent.org/cathen/07783a.htm
Nice encyclopaedia reference on indulgences from the Catholic Encyclopaedia.
I'm kinda chuckling at old and tired's answer. He is sounding old and tired. :^D
To be more precise, the scandal at the heart of Luther's ire was the practice of *selling* indulgences. Some devious monk was wandering around Germany claiming to give indulgences to anyone who would help him build a church. Rome did agree with Luther that the practice was abhorable, and in fact, the monk, was a con man, not with the authority of Rome.
You have to understand the concept of purgatory: Catholics believe that the souls of those who have faith, but whose faith is not so complete as to have ridded their lives of all sin, must be cleansed of their sin in the after life. This is not a denial of the efficacy of Christ's atonement; this is for those who have ascented to accepting Christ, but who have clung in part to sin. Nor is purgation for sins committed before baptism, I believe, as they are washed fully away at baptism
By accepting certain graces, identified by the Pope, those who call themselves Christians but who are struggling against their depraved will to purify themselves, may receive some measure of purification by participation in acts of contrition and works of mercy. These avts are called "indulgences."