Jn 20:23 states that Jesus gave the apostles the power to forgive (or not forgive). However, where does it say that He allowed priests to absolve people from their sins?
In Acts, that is exactly what the apostles do–forgive the people their sins. Just as when Jesus healed the paralyzed man (to whom He had said, “Your sins are forgiven”) the apostles’ healing of the physically sick demonstrated as well the healing of the ‘spiritual sickness’ of people. St. James also speaks of having those in sin ‘confess’. While ‘private’ confession as we experience today was not so well known, one must consider that the early chuch was not only relatively ‘smaller’, it was also ‘underground’. An apostle or his successor might (given the difficulties of travel of the time and the widespread areas in which they preached) not be ‘available’ to hear what could be dozens or hundreds of personal confessions ‘in private’ for a period of months or even years. At least the acknowledgement of one’s sin in a ‘communal’ setting showed one’s repentence (much as today we ‘confess’ our sins in the Penitential rite at the beginning of Mass).
And since apostolic succession is also demonstrated in Acts (whereby the place of Judas is filled by Matthias), as well as notation of those such as Stephen and the other six who are appointed to help with the community, and later on notations of people like Timothy, we realize that those ‘prebyters’ and ‘elders’ (whom we call today priests and bishops) are heirs to the ‘bind and loosening’ which Jesus gave to His disciples.
It’s not clear what you’re asking, since you use “forgive” and then “absolve”, but I think you’re asking how come priests have the same authority as did the apostles in forgiving sin? Am I right?
If that’s what you’re asking, it is tied up with the power of the Church to bind and loose heaven. If the Church decides to pass along this particular authority given to the bishops down to the priests, then it becomes binding on heaven that this authority has been given to the priests.
19* On the evening of that day, the first day of the week, the doors being shut where the disciples were, for fear of the Jews, Jesus came and stood among them and said to them, “Peace be with you.” 20 When he had said this, he showed them his hands and his side. Then the disciples were glad when they saw the Lord. 21* Jesus said to them again, “Peace be with you. As the Father has sent me, even so I send you.” 22* And when he had said this, he breathed on them, and said to them, “Receive the Holy Spirit. 23* If you forgive the sins of any, they are forgiven; if you retain the sins of any, they are retained.” RSV (Harmony Media, welcome to the Catholic Church, version 3.0, 2005)
Who is Jesus speaking to? What is the context? He has come from the Father, with a commission, and now is commissioning the apostles, with the authority of the Father, through the power of the Holy Spirit. They have the authority to forgive sins because of this anointing of the spirit (the breath). They also have the authority to deny forgiveness as the retention implies withholding not only forgiveness but absolution, since sins not retained are absolved, no longer held against the sinner. He is not imparting this authority to all believers (who nonetheless are obliged to personally forgive those who injure them) but to the apostles whom he has chosen and prepared (the Last Supper discourse being the most immediate preparation) them to receive the Spirit and the consequent authority. Absolution is implied in the use of retention. Absolution means the sins are gone.
A priest cannot offer absolution in confession unless he has the authority from his bishop to do so. This contrasts with consecration, which is valid even if the Mass is illicit - eg a Tridentine Mass celebrated against the bishop’s instructions.
Some sins, like murder, are reserved, and the bishop insists on being consulted about the specific case before they are forgiven.