A large, solid rock that served as a foundation to build something upon that nothing could wipe out calls to mind the end of the Sermon on the Mount:
24 Therefore whosoever heareth these sayings of mine, and doeth them,
I will liken him unto a wise man, which built his house upon a rock:
25 And the rain descended, and the floods came, and the winds blew,
and beat upon that house; and it fell not: for it was founded upon a
So we know that Jesus was familiar with this sort of imagery. The question, then, is what he was referring to in this specific passage?
Catholics claim that this is the point where Jesus established the church, and its authority, in the hands of Peter, naming him the first Pope, the small rock, an individual example of the large rock (the office of Pope that holds the authority over the church.)
And yet this answer feels somewhat unsatisfying. Popes are human too. Peter was human too. Peter was hotheaded and a bit boastful, and he had some serious problems with his faith. When Jesus invited him out onto the water to walk to him, he was actually able to do it, but then, after it had already been proven to him beyond any doubt that he was in the middle of a bona fide miracle, he doubted! Peter the Rock began to sink like a stone and Jesus had to run over and save him from drowning. And who can forget his cowardice in the face of Jesus's trial and crucifixion, denying his Lord three times just hours after he had boasted of his willingness to follow him even unto death? This is not the picture of a solid foundation that will uphold the church no matter what bad weather beats against it!
But if we reject this interpretation, we are under the necessity of providing a better one, because Jesus did still say that he was going to build his church upon "this rock". So the question becomes, what is "this"? For that, we need more context. Let's look back a few verses:
13 When Jesus came into the coasts of Caesarea Philippi, he asked his
disciples, saying, Whom do men say that I the Son of man am?
14 And they said, Some say that thou art John the Baptist: some,
Elias; and others, Jeremias, or one of the prophets.
15 He saith unto them, But whom say ye that I am?
16 And Simon Peter answered and said, Thou art the Christ, the Son of
the living God.
17 And Jesus answered and said unto him, Blessed art thou, Simon
Barjona: for flesh and blood hath not revealed it unto thee, but my
Father which is in heaven.
18 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
Here we see what it is that they were talking about when he said this. Peter was blessed for the testimony he had received, not by men but by revelation from God, of the divinity of Jesus. Men don't understand who Jesus is--they have all sorts of weird and conflicting theories--but by the power of God, men can have the truth revealed unto them. This revelation, being from God, is infallible, and if the Church is built upon it, it can never fall. Simon was named petros because he was the archetype, the first (of his contemporaries at least) to have received this personal revelation from God. (See Matthew chapter 4, where he and his brother Andrew are named as the first two of Jesus's disciples.)