chilehed's response was very good and I'd like to add to it slightly
The Sacrament of Reconcilliation is well rooted in Sacred Scripture. Let's start with John 20:19-23:
On the evening of that first day of the week, when the doors were locked, where the disciples were, for fear of the Jews, Jesus came and stood in their midst and said to them, "Peace be with you." When he had said this, he showed them his hand and his side. The disciples rejoiced when they saw the Lord. Jesus said to them again, "Peace be with you. As the Father has sent me, so I send you." And when he had said this, he breathed on them and said to them, "Receive the holy Spirit. Whose sins you forgive are forgiven them, and whose sins you retain are retained."
When Jesus gave the disciples the power to forgive (and not to forgive) sins, He did it on Easter Sunday. This is significant because of the connection of the Resurrection with spiritual life. Notice he gave the power by breathing on the Apostles. The only other time in scripture that God breathed on anyone was when he breathed life into the first human being (Genesis 2:7). These powerful symbols signify an awesome life-giving power given to the disciples. Notice that Jesus gives the disciples the authority to forgive and not to forgive. This means they need to hear the sins in order to know whether to forgive them or hold them bound. They cant make the determination just by looking at the sinner.
Christ never engaged in unnecessary acts. He didnt give the Apostles this power His own power for no reason at all. He wanted them to use it.
Now well look at 2 Corinthians 5:17-20:
So whoever is in Christ is new creation: the old things have passed away; behold, new things have come. And all this is from God, who has reconciled us to himself through Christ and given us the ministry of reconciliation, namely, God was reconciling the world to himself in Christ, not counting their trespasses against them and entrusting to us the message of reconciliation. So we are ambassadors for Christ, as if God were appealing through us. We implore you on behalf of Christ, be reconciled to God.
Saint Paul explains how the apostles are ambassadors of Christs work of reconciliation. What does this mean but that they share in the ministry of Christ and forgive sins in His name? Also lets look at James 5:13-16:
Is anyone among you suffering? He should pray. Is anyone in good spirits? He should sing praise. Is anyone among you sick? He should summon the presbyters of the Church, and they should pray over him and anoint him with oil in the name of the Lord, and the prayer of faith will save the sick person, and the Lord will raise him up. If he has committed any sins, he will be forgiven.Therefore, confess your sins to one another and pray for one another, that you may be healed. The fervent prayer of a righteous person is very powerful.
James makes clear that the sins of the sick are forgiven in this sacrament of anointing. He specifies that the presbyters (priests) must be called. They obviously had a power the ordinary Christian did not: the power to forgive sins. Otherwise, why didnt James simply ask ordinary, fellow Christians to pray over the sick as is the case in numerous other passages?
We all believe that God uses His ministers as instruments in His physical healing. Why wouldnt God do the same with the undeniably more important spiritual healing?
Return to John 20:21:
"As the Father has sent me, so I send you." The Apostles are to continue the mission of Christ. The essence of that mission is
THE FORGIVENESS OF SINS. Jesus knows our human nature. He provided sacramental confession to give us several important gifts: humility, the certainty of forgiveness, spiritual direction, and help to overcome self-deception and rationalization in matters of sin. Clearly, Christ gave his disciples the power to forgive sin. This power was intended to be passed on, since Christ knew people would sin until the end of time.
In John 15:5, Jesus likened our relationship with him to a vine, he is the vine and we are the branches;
"I am the vine, you are the branches. Whoever remains in me and I in him will bear much fruit, because without me you can do nothing." Every branch is related to every other branch through the vine. What happens to one branch influences every other branch. If one branch becomes ill, neighboring branches become ill. Even branches far away are affected. Spiritual illness comes when we sin. It is impossible to sin and not influence others in society. We may not be aware of the influence, but it is there. Since every sin is social in its effects it affects every other Christian, even every other person Christ established a social means for forgiveness. In confession we relate our sins and sorrow to another human being, who represents both our Lord and the whole community of the faithful.