An eye for an eye is different depending on the context. In a judicial sense, it basically means that punishment should be proportionate to the crime.

"And if a man cause a blemish in his neighbour; as he hath done, so shall it be done to him; Breach for breach, eye for eye, tooth for tooth: as he hath caused a blemish in a man, so shall it be done to him again. And he that killeth a beast, he shall restore it: and he that killeth a man, he shall be put to death. Ye shall have one manner of law, as well for the stranger, as for one of your own country: for I am the Lord your God." Leviticus 24:19-22

However, an individual seeking an eye for an eye is revenge.

"Ye have heard that it hath been said, An eye for an eye, and a tooth for a tooth: But I say unto you, That ye resist not evil: but whosoever shall smite thee on thy right cheek, turn to him the other also. And if any man will sue thee at the law, and take away thy coat, let him have thy cloak also. And whosoever shall compel thee to go a mile, go with him twain. Give to him that asketh thee, and from him that would borrow of thee turn not thou away." Matthew 5:38-42

"Recompense to no man evil for evil. Provide things honest in the sight of all men. If it be possible, as much as lieth in you, live peaceably with all men. Dearly beloved, avenge not yourselves, but rather give place unto wrath: for it is written, Vengeance is mine; I will repay, saith the Lord. Therefore if thine enemy hunger, feed him; if he thirst, give him drink: for in so doing thou shalt heap coals of fire on his head. Be not overcome of evil, but overcome evil with good." Romans 12:17-21