"단" simpley refers to "Grade/ Rank/ Rate"
There is a similar term like "(등)급"
Ex) 너는 태권도가 몇 단이니?
= What rank are you in Taekwondo?
2015년 8월 8일
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단(段) is the rank of the traditional board game Go(바둑)
There are 9 ranks from 1 to 9 단 for professional player of Go.
9 단 is the highest rank of professional player of Go.
Thus, 9단 means "master of some field"
주부9단 means "master of housewife"