In Short, the book of Titus is about setting things right. Paul is writing to Titus to set right what was left undone in the Cretan churches (Titus 1:5).
The first problem Paul addresses within the churches of Crete was their many false teachers (Titus 1:10-16) :
* Unqualified Teachers
* Dishonest Teachers
* Immoral Teachers
* Apostate Teachers
Paul's solution to this problem is for Titus to appoint elders within the churches (Titus 1:5). The churches of Crete seem to have preached the Gospel and gathered believers but were full of controversy and dissension because they didn’t have elders.
Elders are to be appointed to an official position within the church so that they can lead the church by:
* Holding to the faithful message
* Encourage the congregation with sound teaching
* Refute those who contradict sound teaching
In other words, the primary role of an elder is to teach and enforce sound doctrine.