In the New Testament, Jesus admonishes his followers:
"You have heard that it was said, 'Eye for eye, and tooth for tooth.' But I tell you, Do not resist an evil person. If someone strikes you on the right cheek, turn to him the other also. And if someone wants to sue you and take your tunic, let him have your cloak as well. If someone forces you to go one mile, go with him two miles. Give to the one who asks you, and do not turn away from the one who wants to borrow from you." (Matthew 5:38-42, NIV) But I say unto you which hear, Love your enemies, do good to them which hate you,
"Bless them that curse you, and pray for them which despitefully use you. And unto him that smiteth thee on the one cheek offer also the other; and him that taketh away thy cloke forbid not to take thy coat also. Give to every man that asketh of thee; and of him that taketh away thy goods ask them not again. And as ye would that men should do to you, do ye also to them likewise. (Luke 6:28-31. King James Version)
If a person has been slapped in the face by another as an insult or provocation to a quarrel, a Christian ought not to respond by hitting back or otherwise responding hurtfully. Rather, he ought to present the other cheek (the one that has not been slapped yet) and offer to let that cheek also be slapped in the hopes that the other person's conscience would be pricked and would not slap it, thus preventing a quarrel from really getting started.
Scholars of religion classify the New Testament as apocalyptic literature, as the main protagonist (Jesus) is concerned with the immanent end of the world. Jesus taught that the end of world was literally at hand, and that God would literally institute a new kingdom in the days soon ahead; thus his message was to remove worldly concerns from his followers minds to prepare them for the immanent Kingdom of God.
In later years this phrase came to be understood in a metaphorical sense.
Non-Christians have criticised thhis teaching as unworkable in practice, and potentially immoral, as it rewards those who commit acts of violence, without countering them with self-defense or acts of justice. Others counter this teaching can serve justice when used as the philosophy behind passive resistance as practiced by Mohandas Gandhi and Martin Luther King which the praciticer of this tactic turns the other cheek in an effort to turn the aggressors' violence against them.
See also: Sermon on the Mount -- An eye for an eyeCriticism