A recent Vatican document offers the following definition of an indulgence:
1. This is how an indulgence is defined in the Code of Canon Law (can. 992) and in the Catechism of the Catholic Church (n. 1471): "An indulgence is a remission before God of the temporal punishment due to sins whose guilt has already been forgiven, which the faithful Christian who is duly disposed gains under certain prescribed conditions through the action of the Church which, as the minister of redemption, dispenses and applies with authority the treasury of the satisfactions of Christ and the saints".
My guess is that most outside observers thing that and indulgence is the forgiveness of the guilt of sin directly and not "the temporal punishment due to sins whose guilt has already been forgiven." Perhaps this is easiest to understand using an analogy. If I break my arm and then have the break set, wear a cast until it is healed. I am able to use my arm again but is it as good a new? The answer is no. My arm is weaken by this experience. This is paralleled to what happens in the soul. I have obtained forgiveness but my past sinful behavior has left my soul weak and filled with imperfections that need to be healed by God's grace. If I die in friendship with God but still filled with imperfections I will need to be purified by God's love before I can spend eternity in his loving presence. Catholics call this purification purgation or purgatory. We find this purgation by fire (most likely a reference to God's love) in Scripture in 1 Corinthians 3:10-16. Just to be absolutely clear this isn't about "being saved" but about the later divine perfection of the soul. Protestant theologians also believe in this under the heading of the final perfection and glorification of the soul. What is different for some (perhaps most Protestants) is the denial on their part of the role of the Church as a Sacrament of Salvation.
My guess is that it also smacks to some of something mechanistic. Again this is to misunderstand how this works. The penitent receiving the indulgence is enjoined to make their heart right with God seeking sacramental forgiveness for any serious sins, then to receive our Lord lovingly in the Holy Eucharist, and to pledge to abstain from attachment even to less serious sin and false habits in their life. These are called the "normal conditions" which must accompany the successful reception of the indulgence. An indulgence is then a call to holiness and a gift of grace from the Church.
All of this may raise more questions than it answers, but it is rooted in love and relationship and the mystery of the Church.