The "eye for and eye, tooth for a tooth" law was in the Mosaic Law and shows what justice means in the law and that it should not go past that.
I imagine that the people also used this law as a guide in their dealings with each other.
Jesus took that a step further for His followers and was basically saying not to seek vengeance, even if it is within the bounds of justice. To forgive.
I don't see it as a call for pacifism however, just a call for forgiveness and not seeking revenge.
But if everyone forgave everyone else for everything, then how could you have a functioning society? Also, see my post #18 in this thread.