It is special because it is an entirely new thing that starts to form when the Father in heaven reveals to the Apostle Peter the significance of just who Jesus is. As Jesus exclaims in delight to Peter that flesh and blood had not revealed this to him, he goes straight on to declare that he will build his ecclesia.
Due to the internal, spiritual revelation to Peter, an unseen, spiritual formation begins, and all those who are added to this ecclesia of Christ's must have the same revelation from God so that they both understand the significance of Jesus being the Son of God, the Christ, and they confess it. Context shows that individuals like Simon Peter who make that particular confession of faith as to who Jesus is, form that ecclesia. Indeed, only individuals who make that same confession will be built up by Jesus into his ecclesia. And that confession is only enabled by the Father in heaven revealing it to individuals.
The first task is to grasp the meaning of that Greek word, ecclesia, for many people quite misunderstand it, due to the Greek word having been translated “church”.
The English word 'church' is neither a translation nor a transliteration. It falls well short of what the Greek word conveys, which is a word rooted in the verb kaleo, 'to call'. The preposition ek, 'out of', is joined to it, to create a compound which literally means, 'That which is called out'. Kaleo is used 147 times in the New Testament and means 'to call'. This extends to the words kletos (called - 11 times), and klesis (calling - 11 times).
How could anybody get from - that which is called out - to buildings where people go to? Could the English idea of a building that is called "a church" be an attempt to have people think that if they go to services of worship held in such buildings, or who get their names listed on a roll of members who say they belong to that particular church (as opposed to being supportive members of the church building further down the street, or all other church buildings in the city and in the country) that this proves they are Christians?
The first task has been achieved: the word ecclesia means those who are called out. The words 'assembly' or 'congregation' give the sense, but never the word 'church'! The second task is to understand what this calling is, in order to answer whether this "is not just a general group of people gathering themselves together?"
Christians are people who have been called out of this world to form a new gathering - those who belong to Jesus Christ by faith. Can every person attending a service of worship in buildings called 'churches' identify with having been called out of this world to follow Christ? Absolutely not! Some can, but others cannot. That is because the call is distinct, and comes from God, to individuals. He calls them as an act of grace on his part. 'Calling' is not man's calling upon God, but God's calling to men. He chooses who he will call. Consider how clear the New Testament is about this critically important fact. Here is a running list of texts.
"That the purpose of God according to election might stand, not of works, but of him that calleth" (Rom. 9:11). "It pleased God, who separated me from my mother's womb, and called me by his grace, to reveal his Son in me, that I might preach him among the heathen." (Gal. 1:15-16) "And know that all things work together for good to them that love God, to them who are the called according to his purpose." Rom. 8:28
Perhaps the clearest statement proving those two points in this answer is:
"Unto the church of God which is at Corinth, to them that are sanctified in Christ Jesus, called to be saints, with all that in every place call upon the name of Jesus Christ, our Lord... But we preach Christ crucified, unto the Jews a stumbling block, and unto the Greeks foolishness; But unto them which are called, both Jews and Greeks, Christ the power of God, and the wisdom of God... For ye see your calling, brethren, how that not many wise men after the flesh, not many mighty, not many noble, are called: But God hath chosen the foolish things of the world to confound the wise; and God hath chosen the weak things of the world to confound the things that are mighty; and base things of the world, and things which are despised, hath God chosen." 1 Corinthians 1:2 & 23-24 & 26-28 K.J.
There are very many more texts that could be cited to continue this massive theme running through the New Testament: God chooses those whom he will call out of the world and into fellowship with Christ Jesus, and fellowship with fellow believers in Christ. Those individuals - collectively - constitute the ecclesia of Christ.
Not a single unbeliever can be reckoned in their number, for it is God who does the calling and Christ does the symbolic building. Those so called then go on to call upon the name of God and Christ, but they would never have chosen to join with such a mixed company as Christ builds up, together, in fellowship. People who gather themselves together do so for reasons such as, mutual standing in society; exclusive elevation of a peer group; getting a specific common goal achieved, from finding a partner to making a powerful team. But the group of believers gathered by Christ worship together in such a way that unbelievers coming into their midst are convicted, and declare that God is truly among them. See 1 Corinthians 14:24-25. They see the difference between those called out of the world, and those who are part of the world (themselves). Those called out of the world by God have made the same declaration of faith Peter made about just who Jesus is, and those ones throughout the centuries constitute the ecclesia, the spiritual 'body' of Christ. They are special because unless God had revealed to them how special his Son is, causing them to declare that in faith, they would never have congregated together in fellowship.
