As we seek to answer your good question, let’s start with the verse you mentioned in your question.  To get a good understanding of why the Lord spoke of His church in this verse, let’s read Matthew 16:13-18, “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? And they said, Some say that thou art John the Baptist: some, Elias; and others, Jeremias, or one of the prophets. He saith unto them, But whom say ye that I am? And Simon Peter answered and said, Thou art the Christ, the Son of the living God. And Jesus answered and said unto him, Blessed art thou, Simon Bar-jona: for flesh and blood hath not revealed it unto thee, but my Father which is in heaven. 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.”

In this time alone with His disciples, the Lord Jesus asked them about what was being said about Him.  The Lord asked an important question, “WHOM DO MEN SAY THAT I THE SON OF MAN AM?”  By this time, there were many thoughts and speculations about who exactly the Lord was.  Some thought He was John the Baptist raised from the dead. (You can read of the death of John the Baptist in Matthew 14:1-12.)  Some thought he might be Elijah, Jeremiah, or some other prophet.  At this point, the Lord asked another important question, perhaps more important than the first question.  He asked of His disciples, “WHOM SAY HE THAT I AM?”  Peter’s answer to the Lord revealed that he truly knew who the Lord Jesus was.  He said, “Thou are the Christ, the Son of the living God.”  Let me ask you, dear reader, who do you think the Lord Jesus is?  Do you know He is the very Son of God who came to the earth to die to save pitiful guilty sinners such as we? Do you know that?  Do you understand who Christ truly is?  Do you know Him as your Lord?  Is He your savior? 

Upon Peter’s confession of who He is, the Lord declared, “…thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it.”  It is the acknowledgement of the person of Christ that is the foundation of His church.  The Greek word for church is ‘ekklēsía’ and it is defined as a calling out, or an assembly.  It is actually more accurate to translate this word as ‘assembly’, but the word is used 118 times in the New Testament and is translated as church, churches, and assembly.  The church is a called out group of people who know Christ as their savior.  Notice that the Lord said He “will build” His church.  This shows His church had not yet been built or established at that time.

The Lord’s church (the only church spoken of in the Bible) was established in Acts 2, with the coming down of the Holy Spirit to indwell every believer.  (Read Acts 1:6-8 and 2:1-4).  We read of the church in Acts 2:47, which tells us, “And the Lord added to the church daily those who were being saved.” (NKJV).  A person cannot join the Lord’s church.  No, the Lord will add him to His church once he accepts the Lord Jesus Christ as his savior.  While it is possible to join a local church, the only way to be in the true church is to be saved.  The true church has ONLY true believers in it. 

Christ is the head of His church, which is also known as His body.  We read in Ephesians 1:22-23 of the Lord Jesus, “And hath put all things under his feet, and gave him to be the head over all things to THE CHURCH, WHICH IS HIS BODY, the fulness of him that filleth all in all.”  Notice that the church is not an organization.  No, it is an organism.  It is truly the body of Christ…a living, breathing entity.  It is also referred to as the House of God in 1 Timothy 3:15 which says, “But if I tarry long, that thou mayest know how thou oughtest to behave thyself in THE HOUSE OF GOD, WHICH IS THE CHURCH OF THE LIVING GOD, the pillar and ground of the truth.”  The church is not a building.  No, it is every single person who knows Christ as his or her savior.

We read in 2 Corinthians 1:1, “Paul, an apostle of Jesus Christ by the will of God, and Timothy our brother, unto the church of God which is at Corinth, with all the saints which are in all Achaia.”  When Paul wrote to the “church of God which is at Corinth,” he was writing to every true believer in that city, for only true believers are part of the church of God.

Christ loves His church and died so that it might exist.  Husbands are exhorted in Ephesians 5:25, “Husbands, love your wives, even as Christ also LOVED THE CHURCH, AND GAVE HIMSELF FOR IT.”   Christ built His church and adds to it daily every time someone believes on Him.  Are you part of His church?  Do you know the Lord Jesus Christ as your savior?  (CC)  (606.4)