It was quoted in The Chrysanthemum and the Sword and appears to be a japanese idiom.
The truth is that no one knows for sure.
That is because the book's author Ruth Benedict simply does not elucidate in the book what the exact Japanese saying is that she translates as "to take one's proper station".
According to what I could gather online, however, many Japanese Benedict scholars seem to believe that the phrase is:
which indeed means "Each takes his proper station."
応分の場を占める （おうぶんのばをしめる） This is the title of the third chapter I found through a google search. It translates more literally to "Occupy the appropriate area" more or less.
But, it's slightly different in the link the person posted above, so I'm not sure which is the original.