This is the first time the word church in this form is mentioned in the Bible. Very interesting, if you ask me, that it was uttered by Jesus Himself. The word church here is Strong's 1577, ecclesia, which means a popular meeting, especially a religious congregation, an assembly, church. Now this word is mentioned 74 times in 73 verses in the New King James, and if you noticed, a building is missing from that definition.
Now that being said, if we really think about this verse, we understand that the word church is first uttered to the world by our Savior. Pretty significant, if you ask me. God is the originator of all things, so it is interesting to me that He introduced this word showing personal ownership of it and stating that it will not be destroyed.
Here we see that Peter is called petros or a stone indicating something smaller. Since the word used here in Matthew 16 is petra, Jesus is stating that His church would be built on Him, Jesus Christ, the stone.
Now this is one of several instances where Jesus Christ is referred to as the Rock. So bringing this all together, when Jesus says that the church will be built upon Him, the chief cornerstone, and it is an assembly and congregation of followers that He has claimed ownership, it is His, not man's, not a group of people, not an institution or denomination of men, not a tradition, not an organization, and not a physical building. It is His. He builds it, sustains it, and leads it.