An expression derived from the Bible; meaning, to love your enemies while resisting them non-violently.
It says, I will not seek revenge because I am stronger than that. I will not respond with shame because I have dignity in Jesus; and not in hurting you.
Turning the other cheek is a powerful response, as it may require a great deal of self-control, which is painful to do in some cases (see example).
I Turn the Other Cheek when my enemies attack or insult me, but now that they're masquerading as me, causing confusion, division, and strife amongst my friends... turning the other cheek has become painfully hard and I feel deeply saddened.