Will I give Achsah my daughter - In ancient times fathers assumed an absolute right over their children, especially in disposing of them in marriage; and it was customary for a king or great man to promise his daughter in marriage to him who should take a city, kill an enemy, etc. So Saul promised his daughter in marriage to him who should kill Goliath, 1-Samuel 17:25; and Caleb offers his on this occasion to him who should take Kirjath-sepher. Profane writers furnish many similar examples.

And Caleb said, he that smiteth Kirjathsepher, and taketh it,.... Which he ordered to be proclaimed through the army that was under his command; and which was done not so much on the account of the difficulty of taking the place, through the number of the inhabitants of it, and its fortifications, which it seems had fallen again into the hands of the Canaanites, since it was taken by Joshua; nor through inactivity, diffidence, and timorousness in himself; but that others, who were officers, and men of valour under him, might gather some laurels as well as himself; and chiefly being under a divine impulse, he ordered this declaration to be made, whereby his brother Othniel, who was to be a judge in Israel, might appear a great man, and fit for such an office; and as an encouragement, he promises as follows:
to him will I give Achsah my daughter to wife; and to be married into the family of the chief prince of the tribe of Judah was a very great honour, as well as no doubt a very large dowry might be expected, and was given with her, and very probably the city of Debir was promised that should be taken. This Achsah seems to be a daughter of Caleb by a concubine, 1-Chronicles 2:48.

OTHNIEL, FOR HIS VALOR, HAS ACHSAH TO WIFE. (Joshua 15:16-20)
He that smiteth Kirjath-sepher--This offer was made as an incentive to youthful bravery (see on 1-Samuel 17:25); and the prize was won by Othniel, Caleb's younger brother (Judges 1:13; Judges 3:9). This was the occasion of drawing out the latent energies of him who was destined to be the first judge in Israel.

To wife - Which is to be understood with some conditions, as, if he were one who could marry her by God's law; and if she were willing; for though parents had a great power over their children, they could not force them to marry any person against their own wills. He might otherwise be an unfit and unworthy person; but this was a divine impulse, that Othniel's valour might be more manifest, and so the way prepared for his future government of the people, Judges 3:9.