v 2. Timothy was well thought of by the believersin Lystra and Iconium, so Paul wanted him to join them on their journey.
Having left the young man Mark behind it seems that Paul was on the lookout for another younger person to work with him, whom he could mentor and see equipped for the work of mission. Paul happens upon the young man Timothy, who already had a good reputation among the local churches. The fact that he was from a mixed cultural background, a Jewish mother and a Greek father, it would seem that he was well-suited to mix with people of diverse beliefs and cultures. He travelled widely with Paul, and we find his name turning up in all kinds of contexts.
Here is a list of some of the occasions his name crops up: it is worth looking at these, and then go on to see where else he pops up in the story. Acts 17:14-15; Acts 19:22; 1 Corinthians 4:17; Philippians 1:1; Philippians 2:19-22; 1 Thessalonians 1:1; 1 Thessalonians 3:6.
From these and other references you get a picture of Timothy as the team member who travels as Paul’s representative, teaching and encouraging the churches that Paul had founded in his earlier travels.
Paul has the reputation of being an energetic and determined preacher and church founder, but in all that work he was effectively supported by a team of people, including Timothy, who went where Paul sent them, and engaged with the churches to help build and strengthen their life.