My intuitive understanding of it is that so long as the penitent does not deliberately lie about the sin, his contrition, or about his purpose of amendment, the sin is actually forgiven by God if and when the priest absolves, or not forgiven if he does not absolve. It is the same principle as with the Holy Eucharist: it becomes the Body, Blood and Divinity of Christ when the priest validly proclaims the Institution (Epiclesis in the East) regardless of the disposition of the priest or the communicant, but it confers grace on the communicant if he is properly disposed.
I am pinging a few among the many who know more than I on the subject, to correct me if I am wrong.
I’d say that the priest offers reconciliation to the Church through absolution of sins; that God actually forgives the sins. And, here, I mean “reconciliation” in a sense almost akin to “reunification.”
In the first century, the community as a whole shunned those who sinned gravely and unrepentantly. When the person confessed their sins to the community, and absolved to amend their behavior, they were welcomed back into participation.
As the Christian community became more established, inherent conflicts arose. What if one person confesses adultery with another Christian, for instance? How can the 2nd person’s confession be anything other than coerced, if that person has known nothing but the Christian community his entire life? The solution was to permit the presbyter to represent the entire community in offering discrete absolution, permitting each sinner the opportunity to come forward as their conscience dictated.
Now, the person freely confesses their sins, permitting their consceince the opportunity for genuine contrition and amendment, so that they may worthily receive the blood of Christ for the atonement of their sins. However, the priest acts as the gatekeeper, so that such a sign of forgiveness is not received without having been reconciled with the Church. The sign can be forged through illicit reception of the Eucharist, but this is itself a very grave sin. (What good does it do to have one sin forgiven, while assuredly sending oneself to Hell?)