it means like do u know when people say talk to the hand its just like that turn the other cheek is you gone go the right way instead the wrong way so this is an example: if u get in trouble do u wanna keep getting in trouble or u wanna stop.
Turning the other cheek means not to return insult for insult in retaliation, which is what most people expect and how worldly people act. Responding to hatred with love just might grab someone's attention and afford us a chance to share the gospel. When we respond in a manner that is unnatural, it displays the supernatural power of the indwelling Holy Spirit. Jesus was the perfect example because He was silent before His accusers and did not call down revenge from heaven on those who crucified Him. Read more: http://www.gotquestions.org/turn-other-cheek.html#ixzz2R23ZtOB1
Annie said it perfectly. Jesus was telling people that if someone slaps your cheek, offer your other cheek for them to slap. It means DO NOT RETALIATE. Be the bigger person. When attacked don't attack back. It will stop the argument cold.