This is a good question.

Unfortunately, many people think church is just plural for Christians. This is not the case.

I think there are two errors which must be avoided when talking about "what makes a church a church":

1. Over abstraction of the church as a "theory". What I mean by this is that the "organism" of the church is emphasized over and against the "institution of the church". A radical "Priesthood of every believer" sees the church primarily as a loosely affiliated universal body of believers. On this view church is simply when "two or more are gathered in Christ's name". Of course, this fails to take into account the many ways the church is also required to be structured, per the NT Pastoral Epistles
2. Over particularization of the church as a concrete institution: This is what happens when the "one body" is emphasized to the exclusion of the "many parts" imagery of the church. I think you see this in chruches where "the work of ministry" is delegated only to the "officers" of the church. In my super biased opinion, the 3-fold office view of TE, RE, and Deacon falls into this error. One man in my church said he does not believe any ministry belongs to members of the church; only to her officers.

I think the best approach is to understand the church as "God's worshiping assembly". We see this as early as Genesis 4:26 when "at that time the men began to call on the name of YHWH". This small group of men turns into an entire people Exodus 7:16, "Let my people go, so that they may worship me in the wilderness." This idea is carried all the way up through the New Testament:

In 1 Corinthians 11:18, we read of instructions for “when you come together as a church,” indicating that there was a unique gathering “as a church” that was not the same as a few Christians hanging out and talking about Jesus. Hebrews 10:25 commands us not to neglect meeting together (literally, “do not forsake the assembly of yourselves”). The word for “meet together,” episynagogen, refers to the formal gathering of God’s people for worship, not just friends listening to sermon downloads in the same room or engaged in an inductive bible study. [Source]

Following Berkhov and Kuyper after him, the church is 100% organism and 100% institution. The Bible never chooses between these two. It is both "body" and "temple". I could go on, but if you are interested in reading all about the Biblical Theology of the Church, please see Ed Clowney's article here.