Well, lets look at the scripture.
Jesus has gathered his apostles and asks them who they think he is. They give the answers they've been hearing from the crowd and tell Jesus some think he's John the Baptist, some Elias, others Jeremiah, etc. Jesus asks, but who do you say that I am and Peter boldly proclaims:
"Thou art the Christ, the Son of the living God."
After a brief line explaining how Peter knew this, Jesus then says:
"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..." (See Matthew 16).
Jesus clearly proclaims he is building a church and Peter was given the authority or keys of the kingdom (which to me equals the power to organize and run said church).
My religion teaches that we have this same authority passed from Peter to a modern day prophet and thus, we are the same organization that Christ established when he was on the earth.