Jamieson, Fausset and Brown on Matthew 5:38

38. Ye have heard that it hath been said--(Ex 21:23-25; Le 24:19, 20; De 19:21).

An eye for an eye, and a tooth for a tooth--that is, whatever penalty was regarded as a proper equivalent for these. This law of retribution--designed to take vengeance out of the hands of private persons, and commit it to the magistrate--was abused in the opposite way to the commandments of the Decalogue. While they were reduced to the level of civil enactments, this judicial regulation was held to be a warrant for taking redress into their own hands, contrary to the injunctions of the Old Testament itself (Pr 20:22; 24:29).