I can't quite figure out what "industrious" children should be...

It means the same as ""diligent, hard-working"
In Merriam-Webster it says: ""habitually active or occupied ""
The American Heritage Dictionary says: dj. Assiduous in work or study; diligent. See Synonyms at busy

I know this...theory.
But seriously, who says this about children in your country ?
How natural is that ? It really sounds like xeroxed Japanese...

I heard it in school as a child. Perhaps the word is not used as often as it should be; I would say it has the same low frequency as the word "diligent". But I stand corrected by a quick google search which showed a site from the "Primary School Counseling Blog""
Raising Industrious Children
Posted on April 30, 2015
The Primary School character word for May is “Industrious: Hard Working.” How do we teach our children to be hard-working, independent, and responsible?
I rest my case:)

"Primary school counselling" from Singapore or from "Communist" China ?

This sentence sounds natural enough to me.

Google Ngram Viewer
https://books.google.com/ngrams...trious%3B%2Cc0