Without the keys to All Saints, we would not be able to open the safe to get to the various eucharistic vessels, so the keeper of those keys has quite a responsibility: he or she can provide or prevent access to the Sacrament. This is why the keys are usually in the possession of the Rector, and at the moment are most likely waiting with a Church Warden for the next incumbent, on whose appointment they will be ceremonially handed over to him or her. Even symbolically, they represent a certain authority.
According to Matthew, Jesus gives such an authority especially to Peter. By extension, it is given to all the Apostles, entrenched as they are in the shared bedrock of Peter's faith in Christ. The precise nature of that authority, referring back to Isaiah 22, is as legitimate stewards of the truth of the Kingdom of Heaven, which in many parts of Matthew means the same thing as the Church. The Church has the authority not to declare new truths, but to declare the truth of the Law that it has been given in Christ.
We can listen to that truth, grounded in the faith of the Apostles in Christ, or we can reject it. We can find other authorities for our lives. Some are no doubt better than others. We can look around the world, especially the Middle East at the moment, and judge these various authorities by their fruits; but it is instructive to remember that God judges us by exactly the same criterion, which is the living Law of Our Lord Jesus Christ.