And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it [Matt. 16:18].
Let us look at this verse carefully. On what rock did Jesus build His church? There are those who say that it was built on Simon Peter. Well, obviously it was not, because there is a play upon words here. In the original Greek it is, “Thou art Petros [a little piece of rock], and upon this petra [bedrock] I will build my church.” There are others who hold that Christ is building His church upon the confession that Simon Peter made. I don’t agree with that at all.
Who is the Rock? The Rock is Christ. The church is built upon Christ. We have Simon Peter’s own explanation of this. In 1 Peter 2:4, referring to Christ, he writes, “To whom coming, as unto a living stone, disallowed indeed of men, but chosen of God, and precious.” And he remembers Isaiah 28:16, “… Behold, I lay in Sion a chief corner stone, elect, precious: and he that believeth on him shall not be confounded” (1 Pet. 2:6). The church is built upon Christ; He is the foundation. “For other foundation can no man lay than that is laid, which is Jesus Christ” (1 Cor. 3:11). Christ is the stone, and He says on this rock He will build His church. The church was still future when the Lord made this statement. And please don’t tell me there was a church in the Old Testament because the church did not come into existence until after the death, resurrection, and ascension of Christ, and the sending of the Holy Spirit. There could not have been a church until all of these things had taken place. “I will build my church”—this was future.
The “gates of hell” refers to death. The word used for hell is the Greek word hades, the sheol of the Old Testament, which refers to the unseen world and means “death.” The gates of death shall not prevail against Christ’s church. One of these days the Lord Himself shall descend from heaven with a shout. That shout will be like the voice of an archangel and like a trumpet because the dead in Christ are to be raised. The gates of death shall not prevail against His church.
And I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven: and whatsoever thou shalt loose on earth shall be loosed in heaven [Matt. 16:19].
What are the keys of the kingdom of heaven? Were they given only to Simon Peter? No, Jesus gives them to those who make the same confession made by Peter, those who know Christ as Savior. If you are a child of God, you have the keys as well as any person has the keys. The keys were the badge of authority of the office of the scribes who interpreted the Scriptures to the people (see Neh. 8:2–8). Every Christian today has the Scriptures and, therefore, the keys. If we withhold the Word, we “bind on earth”; if we give the Word, we “loose on earth.” No man or individual church has the keys—to the exclusion of all other believers. We have a responsibility today to give out the gospel because it is the only thing that can save people. This is a tremendous revelation. Who is sufficient for these things? You and I have a responsibility that is awesome indeed!
Then charged he his disciples that they should tell no man that he was Jesus the Christ [Matt. 16:20].
The Lord made this request because the mere knowledge of who He is will not save you. To find salvation you must know who He is and what He did and accept Him by faith.
McGee, J. Vernon: Thru the Bible Commentary. electronic ed. Nashville : Thomas Nelson, 1997, c1981, S. 4:92-93
 

16:18 on this rock. The word for “Peter,” Petros, means a small stone (John 1:42). Jesus used a play on words here with petra which means a foundation boulder (cf. 7:24, 25). Since the NT makes it abundantly clear that Christ is both the foundation (Acts 4:11, 12; 1 Cor. 3:11) and the head (Eph. 5:23) of the church, it is a mistake to think that here He is giving either of those roles to Peter. There is a sense in which the apostles played a foundational role in the building of the church (Eph. 2:20), but the role of primacy is reserved for Christ alone, not assigned to Peter. So Jesus’ words here are best interpreted as a simple play on words in that a boulder-like truth came from the mouth of one who was called a small stone. Peter himself explains the imagery in his first epistle: the church is built of “living stones” (1 Pet. 2:5) who, like Peter, confess that Jesus is the Christ, the Son of the living God. And Christ Himself is the “chief cornerstone” (1 Pet. 2:6, 7). church. Matthew is the only gospel where this term is found (see also 18:17). Christ called it “My church,” emphasizing that He alone is its Architect, Builder, Owner, and Lord. The Gr. word for church means “called out ones.” While God had since the beginning of redemptive history been gathering the redeemed by grace, the unique church He promised to build began at Pentecost with the coming of the Holy Spirit, by whom the Lord baptized believers into His body—which is the church (see notes on Acts 2:1–4; 1 Cor. 12:12, 13). the gates of Hades. Hades is the place of punishment for the spirits of dead unbelievers. The point of entry for such is death. This, then, is a Jewish phrase referring to death. Even death, the ultimate weapon of Satan (cf. Heb. 2:14, 15), has no power to stop the church. The blood of martyrs, in fact, has sped the growth of the church in size and spiritual power.

16:19 the keys of the kingdom of heaven. These represent authority, and here Christ gives Peter (and by extension all other believers) authority to declare what was bound or loosed in heaven. This echoed the promise of John 20:23, where Christ gave the disciples authority to forgive or retain the sins of people. All this must be understood in the context of 18:15–17, where Christ laid out specific instructions for dealing with sin in the church (see note on 18:15). The sum of it all means that any duly constituted body of believers, acting in accord with God’s Word, has the authority to declare if someone is forgiven or unforgiven. The church’s authority is not to determine these things, but to declare the judgment of heaven based on the principles of the Word. When they make such judgments on the basis of God’s Word, they can be sure heaven is in accord. In other words, whatever they “bind” or “loose” on earth is already “bound” or “loosed” in heaven. When the church says the unrepentant person is bound in sin, the church is saying what God says about that person. When the church acknowledges that a repentant person has been loosed from that sin, God agrees.
Gr. Greek
MacArthur, John Jr: The MacArthur Study Bible. electronic ed. Nashville : Word Pub., 1997, c1997, S. Mt 16:18

Matt. 16:19

Because Jesus triumphed over Satan at the cross, the believer can claim victory over Satan in daily battles. A Christian is indwelt with the triumphant power of the Holy Spirit and has the privilege of exercising a divine authority more powerful than the authority of Satan (1 John 4:4). Through the power of the Holy Spirit, we can restore and release someone who has been bound, by exercising the higher authority of the Holy Spirit.
How can we bind Satan by the power of the Holy Spirit? There are three things we must have and use.
1. The name of Jesus
The Bible tells us to pray in Jesus’ name (John 16:23). Throughout the New Testament, the apostles heal and do the works of the Lord in Jesus’ name (Acts 3:6). You and I transact spiritual business, so to speak, by using the currency of the name of the Lord Jesus Christ. When we ask in Jesus’ name, we are saying to the Father, “Jesus would have asked this if He were physically here now.” Can you imagine what would happen to the church if believers took God at His Word and appropriated the power of the Holy Spirit?
2. The blood of Jesus
We dare not come boldly into battle with Satan without the protection of the shed blood of Jesus Christ. Throughout the Scriptures, the shed blood is the symbol of protection and of our redemption. The blood of Christ’s sacrifice paid the price of sin and eternally broke the power of Satan over us.
3. The Word of God
Jesus countered the temptation of Satan by quoting Scripture: “It is written.” He confronted Satan in spirit-to-spirit combat using the Word of God. We must rely on the guidance of God’s Word.
The power to defeat Satan is available to every believer. Every one of us has the ability to deal with Satan by the almighty, supernatural power of God. We have the right to declare Satan bound, his work restricted, and the prisoner set free.
Stanley, Charles F.: The Charles F. Stanley Life Principles Bible : New King James Version. Nashville, TN : Nelson Bibles, 2005, S. Mt 16:19