What does this mean? Well certainly we can say one thing that it doesn’t mean is that there is any priestly absolution. It does not mean that the apostles were given the power to forgive sins or even to declare the forgiveness of sins to people in an authoritative way.
Christ in this statement gives the apostles and all the church the authority to state the terms of eternal life very clearly. We have the authority to make those kinds of statements very clearly, so through us sins are forgiven or retained through the declaration of the gospel. That is the obvious and the plain sense, and the only sense that doesn't make Scripture contradict itself.
Among sounder students of the Bible there are broadly two views about this. One is that given above. The other too quickly links these words with the words of Christ in Matthew 18, and says it means something like this: the disciples are receiving instructions for the administration of the future community, the church that will come about through their preaching. They are being given instructions as the future first officers of those churches about how to discipline congregations and receive people and expel them, and so through the apostles the church is given authority to exercise discipline. Well of course true churches of Christ sadly sometimes do have to exercise discipline if there is unworthy conduct and unworthy members, but that has nothing to do with this.