"A remission before God of the temporal punishment due to sins whose guilt has already been forgiven..." 

 
All sin has two consequences or penalties: eternal, meaning the effect it has on our relationship with God and where we spend eternal life (whether we go to Heaven or Hell), and temporal, meaning sin's lingering effects or damage to our souls or to others. Only God can forgive the eternal guilt of sins; we cannot earn this by anything that we do. 
 
In Confession, we receive the forgiveness of our sins and our friendship with God is restored, which repairs the eternal punishment for sin. Yet even when the Lord has forgiven us, the temporal effects of our sins still remain, and these can be repaired through prayer, penance, and other good works, which make the restitution or justice that is due for the sin.  This is why priests usually assign penance as part of Confession; it's a concrete action that helps repair the temporal damage of the sin. 
 
Temporal consequences for sins can be remitted before death on Earth and after death in Purgatory. Souls who die in God’s friendship but who still must fulfill the temporal justice that their sins demand go to Purgatory, since nothing unclean within us can enter Heaven. 
 

"...which the faithful Christian who is duly disposed gains under certain prescribed conditions..." 

To gain an indulgence, a person first has to have the right disposition to receive it, which means being baptized and in a state of grace. Once we have that disposition, an indulgence lets us receive remission of the temporal consequences of our sins (their eternal guilt having already been forgiven in Confession) by carrying out a work prescribed by the Church. Some works (such as Eucharistic Adoration for 30 minutes, praying the Rosary, and making the Way of the Cross) are always eligible for an indulgence, and maybe you already do these regularly. For special times and events, the Church designates other works for indulgences.
 

"...through the actions of the Church which, as the minister of redemption, dispenses and applies with authority the treasury of the satisfactions of Christ and the saints." 

 
How exactly do we receive that remission of temporal guilt when we get an indulgence? Where does it come from? Any good work done in cooperation with God’s grace can heal some of the temporal consequences of sin. But since we are all one body in Christ, the good works of those in Heaven can also benefit the faithful on Earth and in Purgatory. To encourage certain works on Earth, the Church adds an indulgence to them, taking works that are already good and magnifying their healing effect through the infinite merits of Jesus and the saints. 
 
That's the essence of an indulgence: When we perform a prescribed work under the right conditions, the spiritual goods of the Communion of Saints ("the treasury of the satisfactions of Christ and the saints," in our definition) are applied to the temporal guilt of the sins of those on Earth or in Purgatory.  
 
There are two types of indulgences: partial and plenary. A partial indulgence remits a part or portion of the temporal punishment due to forgiven sin. A plenary indulgence remits all of the temporal punishment due to forgiven sin. The grant of the indulgence will specify the type of indulgence attached to the specific work.