What makes a group of believers a local church?

This testimony is true. Therefore rebuke them sharply, that they may be sound in the faith, not devoting themselves to Jewish myths and the commands of people who turn away from the truth.
Titus 1:13-14

Paul left Titus on the island nation of Crete to bring order and final form and functionality to the bands of believers there. He left him to establish local churches. This was a big task. And in the first chapter of this epistle we see two clear challenges: leadership development and doctrinal clarity.

The believers were suffering from a deficiency in biblical eldership. Titus was instructed to go town to town, and where there were believers, biblical elders were to be appointed as qualified men were trained. I find it interesting that the phrase is "appoint elders in every town", and not "in every church". There is subtle clue here. These groups of believers needed to be organized into churches. Elders were crucial to that process. I might go so far as to say that you do not have a functioning local church until there is elder qualified leadership appointed within it.

The elders could assist Titus in the second task of clearing up the doctrinal controversies raging across the island. Judaizers had gotten involved with the bands of new Christians. They were mixing law and grace. They were confusing the believers with commands of legalism and Jewish mythology. It sounds like these Gentiles were getting trapped in some sort of weird kabbalistic teaching that was starting to dominate the Christian community. Titus, along with qualified men who would organize churches under elder shepherding, would have to take the problem on boldly!

Paul does not mince words. The method for shutting down doctrinal madness is clear: "rebuke them sharply". The goal is orthodoxy: "that they may be sound in faith". Good biblical rebuke on false teaching has the goal of restoring the purity of the gospel. These Christians had unwittingly swallowed the lies. They lacked discerning shepherds to guide them. Paul knew the key to churches getting established in Crete was strong elder leadership coupled with doctrinal clarity and rebuke of heretical teaching.

The beauty of the plain understanding of the New Testament is that the same pattern works today. The gospel reaches the world through local churches with strong loving shepherding elders, and a strong gospel conviction that clearly proclaims and lives out biblical doctrine and practice.