Jesus often spoke to the people in terms that they could understand: using parables or referencing things they already knew. He does this in Matthew 5:38. Here Jesus makes reference to the Old Testament which the people would have been familiar with and He expounds upon it to teach them something new. “You’ve heard it said ‘An eye for eye and tooth for tooth’. “But I say to you, don’t resist an evil person; but whoever slaps you on your right cheek, turn the other to him also.” Jesus is proclaiming that He is now talking which trumps what they had heard before “I say to you…”.
Jesus is teaching practically the opposite of what the people had known to be true: one was justified in retaliation to the same degree that they had been mistreated. Now Jesus is saying, NO, one is not justified in retaliation. If we are wronged then so be it, we do not have the recourse of repaying the mistreatment with evil. What is the underlying principle Jesus is teaching: absolute Love, no matter the situation or person.