Under the Old Law in the Old Testament there are certain precepts to establish and maintain relationships. The ceremonial commands are about the relationship with the Other or God: establishing, nourishing and restoring when lost a good relationship.
Christ comes to restore and elevate this relationship from one of creature to Creator to one of children to Father. We have discussed Baptism as the beginning of this restoration - a remaking - but as noted in the comments on that post, people still sin. Our relationships need nourishing and they still need restoring when we mess them up.
The sacrament of Reconciliation or Confession does just this - reconciles us to God and to each other in the Church, the Body of Christ, following our breaking of this tie.
Why do we need to speak to a priest about our failings in order to be reconciled?
To make it real. Part of our tendency to sin is our capacity for self-deception. We hide from ourselves our motivations, our failings, our fault. Speaking our fault brings it to reality and lets it go.
This is real reconciliation. It is real healing for this incomparable relationship with our Father who is in heaven.
- For I am sure that neither death, nor life, nor angels, nor principalities, nor things present, nor things to come, nor powers, nor height, nor depth, nor anything else in all creation, will be able to separate us from the love of God in Christ Jesus our Lord. (Romans 8.38-39)