The term "Pope" signifies the head Bishop of the Catholic Church. Catholics consider Peter the first Bishop of the Catholic Church. Let us look at Mt. 16:18-19:
(Mt. 16:18-19): 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. 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 loosen earth shall be loosed in heaven.
It is interesting to note that in Mt. 16:18-19 Jesus quotes Isaiah 22:21-22:
(Isaiah 22:21-22) - And I will clothe him with thy robe, and strengthen him with thy girdle, and I will commit thy government into his hand and he shall be a father to the inhabitants of Jerusalem, and to the house of Judah. And the key of the house of David will I lay upon his shoulder; so he shall open, and none shall shut; and he shall shut and none shall open.
What does this quote mean? Jesus is referencing Isaiah in order to show that authority is being passed down not only in the Old Testament but also in Jesus' words "thou art Peter, and upon this rock I will build my church." It is a clear indication of apostolic succession. Jesus will "build" his church but it will not be finished being built. There will be those who will follow.
Let us look at Revelation 1:18 and what "keys" signify.
(Rev. 1:18): I am he that liveth, and was dead; and behold, I am alive for evermore. Amen; and have the keys of hell and of death.
Who holds the keys in Revelation? God! Just as Jesus gave the apostles the power to cast out demon's in his name.
By Jesus giving Peter the keys to the kingdom of heaven, he is giving him the power to do as he did while he was on earth, such as forgiving sins, making decisions about the church and the faith. Jesus continues by saying, "whatsoever thou shalt bind on earth shall be bound in heaven: and whatsoever thou shalt loosen earth shall be loosed in heaven." Jesus is telling Peter as ruler of the church on earth his decisions on earth will be also recognized in heaven. Let us look also at John 21:15-17, Jesus singles out Peter as tell him 3 times to feed his sheep:
(John 21:15-17): So when they had dined, Jesus saith to Simon Peter, Simon, son of Jonas, lovest thou me more than these? He saith unto him, Yea, Lord, thou knowest that I love thee. He saith unto him, Feed my lambs. He saith to him again the second time, Simon, son of Jonas, lovest thou Me? He saith unto him Feed my sheep. He saith unto him the third time, Simon, son of Jonas, lovest thou me? Peter was grieved because he said unto him the third time. Lovest thou me? And he said unto him, Lord, thou knowest all things; thou knowest that I love thee. Jesus saith unto him, Feed my sheep.
What is Jesus trying to tell Peter when He states, feed MY sheep? MY sheep, are what? They are Jesus' followers. Jesus as head shepherd asks Peter to carry on as the head shepherd of the flock. How will Peter feed the flock? Peter will feed the flock spiritually. Here are some additional verses that confirm Peter's role as head of the church.
(Lk 22:32) - Jesus: But I have prayed for thee (Peter) that thy faith fail not; and when thou art converted, strengthen thy brethren.
(Acts 1:15) - And in those days Peter stood up in the midst of the disciples, and said…
(Acts 2:14) And Peter, standing up with the eleven, lifted up his voice, and said unto them, Ye men of Judaea, and all ye that dwell at Jerusalem, be this known unto you, and hearken to my words:
(Acts 4:8-12) - Then Peter, filled with the Holy Ghost, said unto them, Ye rulers of the people, and elders of Israel…
(Acts 15:7) - And when there had been much disputing, Peter rose up, and said unto them, Men and brethren, ye know how that a good while ago God made choice among us, that the Gentiles by my mouth should hear the word of the gospel, and believe