Briefly, it is hard to do better as a start than these two canons.
Canon 959 In the sacrament of penance the faithful, confessing their sins to a legitimate minister, being sorry for them, and at the same time proposing to reform, obtain from God forgiveness of sins committed after baptism through the absolution imparted by the same minister; and they likewise are reconciled with the Church which they have wounded by sinning.
Canon 992 An indulgence is a remission before God of the temporal punishment for sin the guilt of which is already forgiven, which a properly disposed member of the Christian faithful obtains under certain and definite conditions with the help of the Church which, as the minister of redemption, dispenses and applies authoritatively the treasury of the satisfactions of Christ and the saints.
Since penance is a sacrament it pertains to the living only. An indulgence can be applied to the living or the dead.
Beyond that, I would encourage you to consult the Catechism.
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