What does 2 Samuel 14:11 mean?

She said, 'Please, swear by the Lord your God that my son won't be killed by those seeking revenge.' David answered, 'As surely as the Lord lives, not a single hair on your son's head will be harmed.' 2 Samuel 14:11 - Modern Text Bible

(She pushes for a stronger guarantee, and David gives her his word, invoking God's name for emphasis.)