This is a difficult one for me to explain but I'll try. MOST of the time, "better" (without "off") refers to a state of quality. This is superior to That. It's better. It can also indicate a state of improvement, like when describing a state of wellness. "He was sick, but now he's better." "Better off" is a comparative statement between two possible outcomes. It implies that one circumstance, action or choice will, or did, result in an outcome that is superior to another. "He will be better off if he listens to me!" (He will not do as well if he does not listen to me) "She was much better off without him!" (She is happier or in a better situation than she would have been if she had stayed with him) In your question, the children are not superior to other children, but because their mothers are literate, it is likely that their circumstances (level of education, living conditions, opportunities, etc.) will be.

Don't translate literally. 'Better off' means something like, 'a more advantageous position in life'. For example: "Kids with a college education are better off in life than those who only have a high school education." The same goes for 'worse off' which means 'a less advantageous position in life'

'Better off' is an idiom. These two words always go together. The meaning of better off means to be in a better condition or situation. In the sentence 'why are the children of literate mothers better off ' it means that the children who have literate mothers are in a better situation or condition than those who don't have literate mothers. (Maybe they get more support at home for homework or maybe these children perform well academically due to the condition that their mothers are literate.) Hope this helps.