What does Matthew 16:19 mean?

Jesus is still responding to Peter's simple acknowledgement that Jesus is the Christ––or Messiah––and the Son of the living God. Jesus has said Peter is blessed to understand this, an understanding given to him by God the Father. Jesus then tells Peter that He will build His church on "this rock," meaning the truth Peter just declared, or the declaration of that truth itself (Matthew 16:13–18).

Now Jesus gives authority to Peter to act on His behalf. He has done this before in sending out the twelve to represent Him in Israel (Matthew 10:5–15). Jesus will give this same authority to all twelve disciples both before and after His resurrection (Matthew 18:18; John 20:23).

Jesus describes the authority He is delegating to them as the "keys to the kingdom of heaven." He says that whatever they bind or loose on earth will be bound or loosed in heaven. Only the most trusted servant in the household would be given the keys to the doors of the estate. In handing them over, the master of the house would be sharing His authority to open and close, to lock and unlock, the entrance to His home.

Peter and, eventually, the rest of the apostles, are being assigned a crucial role in introducing the gospel to the world. In Christ's name, they will declare He is the Messiah and that faith in Him is the only entrance into His kingdom. In His name, they will also exercise discipline within the church, setting the standard for both what is true and how that truth will be practiced. When the apostles declare something bound or loosed in Jesus' name, the power that resides in heaven will respond and make it so.

What Jesus is not doing is freeing the disciples to act on their own wisdom and will as they lead His church in the coming years. He is giving them responsibility, authority, and supernatural power to lead the church according to His will and His teaching.