As arrows are in the hand of a mighty man - They are what a parent may rely on for defense in danger, or for help in securing provision for himself and family - as the warrior or the hunter relies on his arrows.
So are children of the youth - Sons in their youth; in their prime and vigor. The comparison of sons with arrows or spears is common in Arabic poetry. See Rosenmuller, Com. in loc. Also Morgenland, in loc.