I can’t say that this is official Church teaching because I don’t know.
In Jewish culture, at that time, it was common to strike someone with their right hand. Some communities had laws that stated if you struck someone with your left hand they could be punished with a ten day banishment from the community. Therefore to hit someone with the right cheek with a right hand it would have to be a backslap. A slap, therefore, to degrade or insult. Not the strike of an equal to an equal.
If you turn the other cheek, you force your abuser to look you in the eye and (hopefully) recognize your humanity. Because, in order to strike with the right hand, the abuser would have to use a closed fist (like an equal) rather than the degrading backslap.
So, I guess the modern day interpretation would be to not fight back and to not back away. Instead, force the other person to look you in the eye and recognize your humanity and that you are both children of God.
I hope this was sort of helpful!