In order to explain this quote, one needs to understand what an eye for an eye means. An eye for an eye refers to the belief that a person who is harmed physically or mentally should be able to enact revenge upon the party who has harmed them.
That being said, if all people were to enact revenge, instead of turning the other cheek, the entire world would become blind. This is based upon the fact that all people, at one time or another, either hurt another person intentionally, or they hurt another person unintentionally. Regardless of intent, all people are hurt. Therefore, if all people are entitled to revenge, the entire world would be blind.