Timothy was “the son of a certain Jewish woman who believed, but his father was Greek.” It is believed, based upon Acts 16:1-3 and 2 Timothy 1:5 and 3:14-15, that Timothy’s father did not become a Christian and may likely have even 
been dead by the time Paul came to Lystra.
Why are we told about Timothy’s father? Perhaps this detail is included to impress the reader with Timothy’s faithfulness in spite of his father’s unbelief. Perhaps it is mentioned to reassure other young people who may have a parent who is not a Christian. Perhaps it is included to encourage Christians not to be dissuaded by a parent’s rejection of the gospel but to remain true to what they “have learned and been assured of” in “the Holy Scriptures” (2 Tim. 3:14-15). Perhaps it is here as God’s plea to place your faith in Jesus and not in a parent’s past choices.
Timothy’s faith is praised (2 Tim. 1:5; 3:14-15), and he is set forth as an example of faith for us (1 Tim. 4:12). In whom have you placed your faith? In a family member? Or in Jesus?