But I trust in the Lord Jesus to send Timotheus shortly unto you, that I also may be of good comfort, when I know your state. For I have no man likeminded, who will naturally care for your state. For all seek their own, not the things which are Jesus Christ's. But ye know the proof of him, that, as a son with the father, he hath served with me in the gospel. Phil.2:19-22
A good summary of St. Timothy's life was given by Pope Benedict XVI in his December 13, 2006 General Audience. You may read it here.
The martyrdom of St. Timothy took place in Ephesus, when angry Pagans murdered him with stones and clubs because he interrupted an annual festival procession in honor of their gods. He preached that they should turn from their dead idols to the Living God through His Son Jesus Christ, and so they fell on him in anger, killed him and dragged his body through the streets.
The Feast Day for St.Timothy is January 24th in the West, but is on January 22nd in the Orthodox Church.