Speaking of or acting out family dysfunction in a public space. Speaking openly of family secrets.; or being overheard by strangers when discussing private matters. ‘Dirty laundry’ represents one’s private deficiencies or family secrets and by airing them out, like laundry in the backyard, you are inadvertently making them public. (Compare to Made a fool of, Stepped in it or Create a scene.)

 “A man on the bus was telling a stranger about his mistress, I personally wish he wouldn’t air his dirty laundry in public.”