This verse has become a part of colloquial English, although most people do not know where the phrase comes from.  It is the fifth of Jesus' seven sayings in Luke 6:27-31 about the unconditional love which should characterise all the citizens of God's Kingdom: love your enemies (v27); do good to those who hate you (v27); bless those who curse you (v28); pray for those who ill-treat you (v28); do not fight back (v29); give without demands (v29-30); treat others as you would like to be treated (v31). Before you think, ‘These commands are impossible’, remember that Jesus demonstrated every one of them. And He certainly did not fight back.

Isaiah 53:7 says, ‘He was oppressed and afflicted, yet he did not open his mouth; he was led like a lamb to the slaughter, and as a sheep before her shearers is silent, so he did not open his mouth.’  Jesus fulfilled that prophecy.  At His arrest Jesus offered no resistance; "Am I leading a rebellion," said Jesus, "that you have come out with swords and clubs to capture me? Every day I was with you, teaching in the temple courts, and you did not arrest me. But the Scriptures must be fulfilled." (Mark 14:48-49).

Israel was dominated by the occupying Roman army.  The soldiers had the right to requisition anything or anybody (Luke 23:26).  Whatever they demanded had to be surrendered; resistance was foolish.  But with other people in the community, workplace or family, the temptation to argue, resist or fight back can be very strong.  Peter would have remembered Jesus’ words because he wrote 1 Peter 2:18 to slaves with harsh taskmasters.  

The disciples, and the early churches, were expected to learn from the words and example of Jesus; and do the same.  They did!  They rejoiced that God had counted them worthy to suffer for Jesus' sake (Acts 5:41).  Stephen was stoned to death offering no resistance (Acts 7:54-60) and James was executed (Acts 12:2).  However, the church grew because their cheerful handling of persecution validated the truth about Jesus, and many others believed. So 'turning the other cheek' is not just passive acceptance of evil, but a positive confidence that Jesus will always have the last word.  So, how does that relate to you in the office, factory, ship, hospital, school, sales room or farm? When others demand more than they should, do you fight back; or do you let your reaction speak for Jesus?