Jesus begins sharing with His disciples the deeper revelation of who He truly is. While the Pharisees and the multitudes offered possibilities of Him being John the Baptist, Elijah, or even Jeremiah, the Heavenly Father wanted the disciples to know that Jesus was more than the promised Messiah; He is God's son, the very essence of God in the flesh. Revelation knowledge from the Holy Spirit came over Peter and he proclaimed this truth by saying, "You are the Christ, the Son of the Living God!" This is a revelation that does not come from intellect or learning, but by divine revelation from above.
Jesus proclaimed that upon this rock (which is the revelation knowledge of Jesus being the Christ, the Son of the living God AND the proclamation of such truth), He would build His church. Don't be fooled into thinking that the church is built on the man Peter, because it is not! It is built on the Savior Jesus! We see this explained by the Apostle Paul in the book of Romans 10 - if you believe in your heart that God raised Jesus from the dead AND you confess Him as Lord, you shall be saved. Revelation and proclamation are the keys to being born again!
The gates of Hell did not, cannot, and never will prevail against Jesus' church. People who are trapped in sin, guilt, and condemnation need deliverance and the church has the authority and power of Jesus Christ to deliver the message and set the captives free. What an awesome privilege and responsibility!