What does Titus 1:5 mean?

Verse 5 explains the background to Paul's letter. Paul and Titus had ministered together evangelizing the people of the island of Crete. Paul later left, with Titus remaining. This took place sometime after Paul's house arrest (Acts 28), which ended around AD 62, and his second Roman imprisonment which likely occurred sometime in AD 65. This second stint is recorded in the book of 2 Timothy.

Titus remained in Crete for two reasons. First, there was unfinished business when Paul left. Titus was the man responsible for completing it. This phrase may be general in nature, with the later parts of the letter offering details of what this unfinished work included. Second, Titus was to "appoint elders in every town…" The good news was that many towns had a positive response to the Christian message. There were likely house churches in each "town," though not necessarily every small village. However, these new churches lacked leaders. Titus was to "appoint" elders. This was not a vote, but rather a process in which Titus selected godly men based on the principles given in verses 6–9.