One of the key words in this passage is the word "rock". The word rock here means a large immovable rock, such as a foundation stone. However, Jesus actually uses a play on words here because the name "Peter" means a small rock. So, what Jesus actually said was "You are Peter (small rock) and on this rock (large foundation stone) I will build my church". Jesus used a similar play on words in John 2:18-22 when referring to Himself as the Temple.
So, who or what is this large rock that Jesus is talking about? Well, we can look to Peter's words for the answer. Peter said "You are the Christ, the Son of the Living God." He is talking about Jesus Himself. It is Jesus who is the foundation stone of the church. The foundation stone of the church is the fact that Jesus is the Christ, the Son of the Living God.
So, we know that Jesus was referring to Himself when He was talking about the Rock. Why, then is he also making reference to Peter as the small rock? The answer is because the Spirit of God was working through Peter. Notice here that Peter did not come up with the conclusion of Jesus being the Christ by himself (not by flesh and blood), but it was God the Father who had revealed it to him.
Therefore, anyone who has been given the revelation that Jesus is in fact the Christ, the Son of the Living God is a small stone being built upon the large Rock. In 1 Peter 2, Peter talks about Jesus as being the living stone, but then also goes on to say that we ourselves are living stones as well. In a way, he is saying that we are 'a chip of the old block'.
Jesus is the Light of the world, but we are also supposed to be light to the world, allowing God's light to shine through us. We are to be like Jesus in many ways, including being a living stone as He is The Living Stone.
1 Corinthians 12:3 says that "no one can say 'Jesus is Lord' except by the Holy Spirit." What this means is that no one will truly be able to see the truth that Jesus is Lord, unless the Holy Spirit first reveals it to them. Peter saw this truth, because God had revealed it to him. Have you come to the realization of this truth? If not, ask God to reveal it to you, so that you too can become a living stone for Him.