Literally 오붓하다 means Cozy or Comportable
so in this sentence it menas "Try to have a comportable conversation(오붓하게 대화를 하기 위해)"
You can use it between friend, however, usually really close friend because 오붓한 대화 can be used when they are close relationship. Also It can be used between family.
Therefore, mostly couple use it ;)