Just like both previous letters which are addressed to a person (Timothy), this letter is also addressed to a person: Titus. Timothy and Titus are not random people. They belong to the fellow workers of Paul. You have learnt some things about Timothy from the book of Acts. If you want to learn about Titus in that book you will search in vain in it. He is not mentioned there. But you can learn about him from some letters of Paul, especially his second letter to the Corinthians. If you read there what Paul says about Titus you will notice that he very much appreciates him.
The work of Titus in Corinth is an example of his dedicated service. From references to Titus in the mentioned letter we can conclude that he became a mature believer through spiritual growth and experience. Paul desired the support of Titus (2Cor 2:12); he experienced comfort through Titus (2Cor 7:6); he knew the joy of Titus and the refreshment of his spirit about the good that he saw in the believers (2Cor 7:13); he knew about the love that Titus had for the obedient believers (2Cor 7:15); he testified to the willingness of Titus of committing himself on behalf of poor believers (2Cor 8:6,16).
He calls Titus his “partner and fellow worker” with the Corinthians (2Cor 8:23). Titus has the same goal like Paul, that’s why Paul appreciates Titus very much in the work for the Lord. He also sees the same unselfishness with Titus which characterizes himself (2Cor 12:18). In both the work and the motives Paul has an exceptional co-worker in Titus.
Because Paul calls Titus his “true child” (Tit 1:4) we may assume that Titus heard the gospel from Paul and came to conversion. It is not clear whether he went together with Paul immediately after that.
The first time we find Titus together with Paul somewhere is in connection with the controversial question of whether believers from the Gentiles should be circumcised (Gal 2:1,3; cf. Acts 15:1-2). In that way Titus is soon confronted with the legalistic pressure that the Jewish believers want to exert on the believers from the Gentiles. He experiences and learns how Paul deals with that. The great counterpart of the law is grace. Titus gets a great impression of that too. One and the other appear to be a good preparation for his task in Crete of which you learn from this letter.
The last reference of Titus in the letters of Paul is in his second letter to Timothy (2Tim 4:10). Without any further explanation Paul writes to Timothy that Titus had traveled to Dalmatia. Most apparently Titus went there to serve the Lord.
When Paul has been in Crete is not to be concluded from the Scripture. It has been assumed that he was accompanied by Titus in Crete after his first imprisonment in Rome. He left after churches came to existence there, but not without leaving his co-worker Titus there, out of his concern for the newly founded churches. The churches have been founded, but still need many instructions with a view to their daily practice. In this view Paul has not been able to finish his work. Titus had to do that. Paul already gave orally as an apostle the authority to Titus and now he does that in writing too.
The assignment to Titus is twofold. He has to set in order what is lacking and he has to appoint elders in each city (Tit 1:5). The letter therefore deals with the maintenance of order in the local churches of God. This order is not seen here so much in relation to the gatherings of the church; it is more about the daily believer-to-believer relationships and their conduct in the world.