I will give you the keys (authority) of the kingdom of heaven; and 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.
This is part of the passage that includes Peter's confession of Christ as the Messiah and the Son of the Living God. Think how happy Jesus must have been, knowing that His crucifixion was coming near, but that He had successfully set His Disciples on a firm path to carry on His work. They recognize Him for who He truthfully is, and He can now begin to prepare them for when He must leave them. He can begin to reveal the Father's plan and the part they will play in it.
He praises Peter for his steadfastness and his faith, and then announces that He, Himself, will be the bedrock or cornerstone of His Church. This is what I picture happening ... Jesus with His hand on Peter's shoulder, saying "Yes, you are a rock". Then, pointing to Himself, saying, "And it is on this rock that I will build My church". Perhaps he laid his hand on his breast, as he did in John 2:19: Jesus answered them, “Destroy this temple, and I will raise it again in three days.”
Then He announces today's passage and their purpose in "the plan"... they will receive the keys to the Kingdom of Heaven! What must they have thought?!? The concept of someone having the keys to anything meant they had the power to open and shut the door to it. But Jesus is telling them they have that power and authority when it comes to the Kingdom of Heaven!
I believe Jesus is telling Peter that he, himself, will open the door to faith, just as he would do to the Jews at Pentecost (Acts 2) and to the Gentiles in the person of Cornelius and his household (Acts 10). Those keys would unlock the blessings and the power of Heaven itself for all those who come to faith in Jesus Christ, the Son of the Living God of Heaven! That faith is a key that unlocks a Divine relationship between Heaven and Earth -- one that cannot be hindered.
But those keys were not reserved for Peter alone! Just two chapters later, in Matthew 18, Jesus repeats the same benefits of binding and loosing, once one unlocks the key to the Kingdom. This time it is directed to the other disciples. But it also pertains to us! When we are obedient to the commands of our Lord, Jesus (in heaven) looses the authority of His Word as it goes forth on earth for the fulfillment of its purpose.
It is important to understand that the expressions “bind” and “loose” were common to Jewish legal phraseology. Whenever a Jew came up against the Law of Moses, that Jewish person was either "bound" or "loosed" in regard to that law. To loose was to permit; to bind was to prohibit. To loose was to free from the law, to bind was to put under the law. Their regular sense, which any Jew would recognize was to allow and to forbid. To bind something was to declare it forbidden; to loose was to declare it allowed. These were the regular phrases for making decisions in regard to the law.
But Jesus has come to fulfill the Law, so Heaven is now the authority to which we appeal -- not the Rabbinic Law. Therefore, whatever we bind (because it goes against the commands of Jesus) has already been declared forbidden; and whatever we loose (that aligns with Jesus and benefits the Kingdom) has already been declared allowable -- and the authority of Heaven stands behind us! It goes without saying that this refers to Kingdom work done in Jesus's Name and in obedience to His Word on earth.
The authority that comes with the keys is still promised to the Body of Christ today. In the powerful words of theologian Charles Spurgeon, "The Lord continues to back up the teaching and acts of His servants, and as long as we abide rightly in Him, we have His sanction to make them valid. The words of His servants, spoken in His Name, shall be confirmed by the Lord, and shall not be, either as to promise or threatening, a mere piece of rhetoric." Hallelujah, that we possess the keys to the Kingdom of Heaven!