Peter and the other disciples were to continue Christ’s work on earth in preaching the gospel and declaring God’s will to men and they were armed with the same authority as He possessed. In Matthew 18:18, there is also a reference to the binding and loosing in the context of church discipline. The apostles do not usurp Christ’s lordship and authority over individual believers and their eternal destiny, but they do exercise the authority to discipline and, if necessary, excommunicate disobedient church members.
It’s not that the apostles were given the privilege of changing God’s mind, as if whatever they decided on earth would be duplicated in heaven; rather, they were encouraged that, as they moved forward in their apostolic duties, they would be fulfilling God’s plan in heaven. When the apostles “bound” something, or forbade it on earth, they were carrying out the will of God in the matter. When they “loosed” something, or allowed it on earth, they were likewise fulfilling God’s eternal plan. In both Matthew 16:19 and 18:18, the syntax of the Greek text makes the meaning clear: “Whatever thou mayest bind upon the earth shall be having been bound in the heavens, and whatever thou mayest loose upon the earth shall be having been loosed in the heavens” (Matthew 16:19, Young’s Literal Translation). Or, as the Amplified Bible puts it, “Whatever you bind [forbid, declare to be improper and unlawful] on earth will have [already] been bound in heaven, and whatever you loose [permit, declare lawful] on earth will have [already] been loosed in heaven.”
Jesus taught that the apostles had a special task on earth. Their words of authority, as recorded in the New Testament epistles, reflect God’s will for the church. When Paul declared an anathema on those who pervert the gospel, then we know that anathema was already declared in heaven (see Galatians 1:8–9).