Regarding John 20:23 and Matthew 16:19 on the forgiving and retaining sins and binding and loosing, John Calvin explains what that power is and how it is exercised:
This command concerning remitting and retaining sins, and that promise made to Peter concerning binding and loosing, ought to be referred to nothing but the ministry of the word. When the Lord committed it to the apostles, he, at the same time, provided them with this power of binding and loosing. For what is the sum of the gospel, but just that all being, the slaves of sin and death, are loosed and set free by the redemption which is in Christ Jesus, while those who do not receive and acknowledge Christ as a deliverer and redeemer are condemned and doomed to eternal chains?
When the Lord delivered this message to his apostles, to be carried by them into all nations, in order to prove that it was his own message, and proceeded from him, he honored it with this distinguished testimony, and that as an admirable confirmation both to the apostles themselves, and to all those to whom it was to come. It was of importance that the apostles should have a constant and complete assurance of their preaching, which they were not only to exercise with infinite labour, anxiety, molestation, and peril, but ultimately to seal with their blood. That they might know that it was not vain or void, but full of power and efficacy, it was of importance, I say, that amidst all their anxieties, dangers, and difficulties, they might feel persuaded that they were doing the work of God; that though the whole world withstood and opposed them, they might know that God was for them; that not having Christ the author of their doctrine bodily present on the earth, they might understand that he was in heaven to confirm the truth of the doctrine which he had delivered to them.
On the other hand, it was necessary that their hearers should be most certainly assured that the doctrine of the gospel was not the word of the apostles, but of God himself, not a voice rising from the earth but descending from heaven. For such things as the forgiveness of sins, the promise of eternal life, and message of salvation, cannot be in the power of man. Christ therefore testified, that in the preaching of the gospel the apostles only acted ministerially; that it was He who, by their mouths as organs, spoke and promised all, that, therefore, the forgiveness of sins which they announced was the true promise of God; the condemnation which they pronounced, the certain jndgment of God. This attestation was given to all ages, and remains firm, rendering all certain and secure, that the word of the gospel, by whomsoever it may be preached, is the very word of God, promulgated at the supreme tribunal, written in the book of life, ratified firm and fixed in heaven. We now understand that the power of the keys is simply the preaching of the gospel in those places, and in so far as men are concerned, it is not so much power as ministry. Properly speaking, Christ did not give this power to men but to his word, of which he made men the ministers.