"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." - Catechism paragraph 1471

When we sin, we offend God and also hurt our souls.  The Sacrament of Confession completely forgives us in the eyes of God and makes the soul clean.  However, a wound can be clean, yet still exist.  This is where the healing process comes in.  Confession is like the disinfectant to remove deadly germs in an infected wound.  Confession is the first step to greater freedom.  The next step is our cooperation with God's grace every day.  By making the right choices, God's grace builds in the soul, and His love, grace, and mercy fill up the souls wounds and will eventually heal the damage completely.  But there will be no total healing unless we stop inviting in the germs and viruses that make the soul weak!  Sin is like those germs and viruses, and there is a special medicine to treat them which can come in two forms.  One form is pleasant, the other is not.  They are indulgences and temporal punishment.

Temporal punishment is suffering permitted by God to give His children the opportunity to make right choices even when they're not easy, become less selfish when it would be easier to think only of ourselves, and become more loving when it would be easier to ignore others.  Jesus said that to follow Him we must deny ourselves and take up our crosses (Mark 8:34).  Our crosses are our ways of suffering.  They are the things that we find unpleasant which require a sacrifice or patience to endure.  As with exercising the body, it is a good type of suffering.  With the right attitude, we will grow and be stronger.  Your soul will grow in virtue and be less selfish because you have to look outside of your own little world and think of and serve others.  At the center of the Gospel is the cross, and that is where Christ's ultimate act of redemption and ultimate act of sacrifice opened the door for salvation for all.  Christians are to imitate that.

The other way the soul can be healed of the after-effects of sin is by indulgences.  Indulgences are good works that remove the temporal punishment due to sin.  They can remove temporal punishment either partially or completely.  How can this be, if our souls become stronger through carrying our crosses?  It is because God's grace is stronger than we ever will be, and He can apply His mercy and healing in any way He desires including by us His children simply asking Jesus to immerse us in it.

A partial indulgence takes care of part of the temporal punishment that would otherwise strengthen the soul in need of a chance to demonstrate virtue.  A plenary indulgence completely heals the damage in the soul due to sin.  Temporal punishment can come either during life on earth, or after death in Purgatory because the Bible says that no sin will enter Heaven, so we will be completely purified at some point before entering Heaven where there is no darkness but only light.  This is all God's mercy, it is the Father's tough love for His children, the Father who will give His children what they need to grow.

Indulgences remove the need for the unpleasant medicine of suffering, and instead gives the soul an easier, pleasant medicine found in the total immersion in God's infinite mercy.  Indulgences come from the spiritual treasury of the Church which is like an infinite reservoir of grace and mercy which Jesus opened up at the Cross.  Included in this treasury are the good works and merits of the saints and the Blessed Virgin Mary.  While they are all finite people, this truth speaks of the glorious mystery that when we unite our sufferings to the Cross of Jesus, we cooperate with God in the redemption of the world, and open the door for grace.

How to obtain indulgences: 

1. Be in a state of grace.  Indulgences heal the wounds of sin, not sin itself.
2. Desire to not sin.
3. Ask God for indulgences.  For example, pray an Our Father and a Hail Mary for this intention.
4. Do the work associated with the indulgence.  For example, many simple prayers or acts of charity bring indulgences with them.  The Church lists these in a brief handbook called the Enchiridion of Indulgences available here:  http://www.ourladyswarriors.org/indulge/

For a plenary indulgence you also need to receive Communion, go to Confession within a week of doing the indulgenced work, and pray for the Pope.  Not all indulgences are plenary indulgences, some are always partial, but one designated plenary will be partial if one of the conditions is missing.