What are indulgences? Didn't the Church sell them?

The teaching. Sin has two consequences: eternal punishment (removed by forgiveness) and temporal punishment, the disorder and attachment sin leaves in us that must be purified here or in purgatory (CCC 1472). An indulgence is "a remission before God of the temporal punishment due to sins whose guilt has already been forgiven," which the Church grants by applying the merits of Christ and the saints (CCC 1471).

The logic. If a boy breaks a window and is forgiven, he still has to help pay for the glass. Forgiveness restores the relationship; reparation heals the damage. The Church, with Christ's power to bind and loose (Mt 16:19), can draw on the infinite merits of Christ and the superabundant merits of the saints, the "treasury of the Church" (CCC 1476-1477), to remit that debt for those who perform a prayerful act with the right disposition.

How to gain one. Typical conditions for a plenary (full) indulgence: sacramental confession, Holy Communion, prayer for the pope's intentions, detachment from all sin, and the indulgenced act itself, such as thirty minutes of Scripture reading or adoration, praying the Rosary in church or with family, or the Stations of the Cross. Partial indulgences are attached to many short prayers. Indulgences can be applied to the souls in purgatory.

The abuse. In the late Middle Ages some preachers, notoriously Johann Tetzel, effectively sold indulgences to fund building projects, which sparked Luther's protest. The Council of Trent condemned "all base gain for securing indulgences" and abolished the office of indulgence-seller in 1567. The doctrine was never the problem; the corruption was. Today no money can be attached to an indulgence at all.