AVENGER. The Hebrew word goēl has a two-sided application of its basic meaning. At heart it is a very gracious word: It refers to the “next of kin” who possesses the right to take on himself whatever need may have overwhelmed his kinsman or kinswoman. We see this at its human best in the Book of Ruth (3:12-13; 4:2-10) and at its highest when the Lord himself is called our goēl (Isa.43.14). But there is a darker side. Suppose someone has committed the ultimate crime against us and we lie dead through murder. What then? The goēl comes to take our part and to exact the vengeance that the law demands (Num.35.11-Num.35.34). This is how the word that means “redeemer” also means “avenger.” OT law was rightly dominated by the concept of equality: an exact equivalence between crime and punishment. It expressed this in characteristically vigorous terms—for example, “an eye for an eye” (Exod.21.23-Exod.21.24; Lev.24.20; Deut.19.21). We should note that these passages all refer to punishments imposed by courts of law and are not rules for private conduct. In the case of murder, where life must be taken for life, the next of kin took up the dreadful duty, carefully circumscribed in his actions by the clear OT distinction between capital murder and accidental manslaughter and by the limitation of vengeance to the murderer only (Deut.24.16).——JAM
International Standard Bible Encyclopedia (1915)
The translation in the Revised Version (British and American) differs in some places from King James Version: Nu 31:3 Revised Version (British and American) "execute Yahweh’s vengeance"; (compare 2Sa 22:48; Ps 18:47; Le 26:25); Le 19:18 Revised Version (British and American) "take vengeance"; Jud 5:2 Revised Version (British and American) "for that the leaders took the lead in Israel" from para`, "to be free, to lead".
In the New Testament avenge is translated from the Greek ekdikeo, "to do justice," "to protect" (Lu 18:3 ff et al.) and the King James Version Re 18:20, krino, "to judge" Revised Version (British and American) "God hath judged your judgment".
Avenger.--That is, the person who inflicts punishment upon the evil-doer for a wrong experienced by himself (from naqam, "to avenge"; Ps 8:2 et al.) or by someone else from ga’al, "to redeem"; (Nu 35:12 ff et al.). In the New Testament avenger occurs only once; "the Lord is an avenger in all things" (1Th 4:6). It was the duty of the nearest relative to execute vengeance upon the murderer of his kin: he became the go’el. With reference to the protective legislation and custom, see Goel. Compare BLOOD; REVENGE, REVENGER.