The following comes from the American Catholic site:
What we know from the New Testament of Timothy’s life makes it sound like that of a modern harried bishop. He had the honor of being a fellow apostle with Paul, both sharing the privilege of preaching the gospel and suffering for it.
Timothy had a Greek father and a Jewish mother named Eunice. Being the product of a “mixed” marriage, he was considered illegitimate by the Jews. It was his grandmother, Lois, who first became Christian. Timothy was a convert of Paul around the year 47 and later joined him in his apostolic work. He was with Paul at the founding of the Church in Corinth. During the 15 years he worked with Paul, he became one of his most faithful and trusted friends. He was sent on difficult missions by Paul—often in the face of great disturbance in local Churches which Paul had founded.
Timothy was with Paul in Rome during the latter’s house arrest. At some period Timothy himself was in prison (Hebrews 13:23). Paul installed him as his representative at the Church of Ephesus.
Timothy was comparatively young for the work he was doing. (“Let no one have contempt for your youth,” Paul writes in 1 Timothy 4:12a.) Several references seem to indicate that he was timid. And one of Paul’s most frequently quoted lines was addressed to him: “Stop drinking only water, but have a little wine for the sake of your stomach and your frequent illnesses” (1 Timothy 5:23).
Titus (d. 94?): Titus has the distinction of being a close friend and disciple of Paul as well as a fellow missionary. He was Greek, apparently from Antioch. Even though Titus was a Gentile, Paul would not let him be forced to undergo circumcision at Jerusalem. Titus is seen as a peacemaker, administrator, great friend. Paul’s second letter to Corinth affords an insight into the depth of his friendship with Titus, and the great fellowship they had in preaching the gospel: “When I went to Troas...I had no relief in my spirit because I did not find my brother Titus. So I took leave of them and went on to Macedonia.... For even when we came into Macedonia, our flesh had no rest, but we were afflicted in every way—external conflicts, internal fears. But God, who encourages the downcast, encouraged us by the arrival of Titus...” (2 Corinthians 2:12a, 13; 7:5-6).
When Paul was having trouble with the community at Corinth, Titus was the bearer of Paul’s severe letter and was successful in smoothing things out. Paul writes he was strengthened not only by the arrival of Titus but also “by the encouragement with which he was encouraged in regard to you, as he told us of your yearning, your lament, your zeal for me, so that I rejoiced even more.... And his heart goes out to you all the more, as he remembers the obedience of all of you, when you received him with fear and trembling” (2 Corinthians 7:7a, 15).
The Letter to Titus addresses him as the administrator of the Christian community on the island of Crete, charged with organizing it, correcting abuses and appointing presbyter-bishops.