In Deuteronomy 15:9 and in Nahum 1:11 the word "Belial" is rendered in our translation by the adjective "wicked." The word means "worthlessness."

(from Barnes' Notes)

Children of Belial - בליעל, from בל bal, not, and יעל yaal, profit; - Sept. ανδρες παρανομοι, lawless men; - persons good for nothing to themselves or others, and capable of nothing but mischief.

Certain men, the children of Belial,.... Which signify either persons without a yoke, who have thrown off the yoke of God's law, and will not submit to it, or unprofitable ones, as wicked men be, both to God, themselves, and others:

are gone out from among you; not locally, but with respect to their religious sentiments and practices, having separated themselves from the people of God, and from the service of the sanctuary, the true worship of God, and a profession of it, and given into the worship of idols:

and have withdrawn the inhabitants of their city; withdrawn them by the force of persuasion from the worship of the true God, and drawn them into idolatry:

saying, let us go and serve other gods; unite as one man in the worship of the gods of the Gentiles:

which ye have not known; this was not said by the children of Belial, but is added by the Lord by way of explanation, showing what gods they were that these men advised them to serve, and confirms the observation made on Deuteronomy 13:6.

The third case is that of a town that had been led away to idolatry. "If thou shalt hear in one of thy cities." בּאחת, not de una, of one, which שׁמע with בּ never can mean, and does not mean even in Job 26:14. The thought is not that they would hear in one city about another, as though one city had the oversight over another; but there is an inversion in the sentence, "if thou hear, that in one of thy cities...worthless men have risen up, and led the inhabitants astray to serve strange gods." לאמר introduces the substance of what is heard, which follows in Deuteronomy 13:14. יצא merely signifies to rise up, to go forth. מקּרבּך, out of the midst of the people.

Certain men, the children of Belial, are gone out from among you, and have withdrawn the inhabitants of their city, saying, Let us go and serve other gods, which ye have not known;

13:13 Children of Belial - It signifies properly persons without yoke, vile and wretched miscreants, lawless and rebellious, that will suffer no restraint, that neither fear God, nor reverence man. From among you - That is, from your church and religion. It notes a separation from them, not in place (as appears by their partnership with their fellow citizens both in the sin and punishment) but in heart, doctrine and worship.

the children...: or, naughty men

13:12-18 Here is the case of a city revolting from the God of Israel, and serving other gods. The crime is supposed to be committed by one of the cities of Israel. Even when they were ordered to preserve their religion by force, yet they were not allowed to bring others to it by fire and sword. Spiritual judgments under the Christian dispensation are more terrible than the execution of criminals; we have not less cause than the Israelites had, to fear the Divine wrath. Let us then fear the spiritual idolatry of covetousness, and the love of worldly pleasure; and be careful not to countenance them in our families, by our example or by the education of our children. May the Lord write his law and truth in our hearts, there set up his throne, and shed abroad his love!