Converse is a more formal way of saying "carry on a conversation." You could converse with your best friend for hours over lunch, but continue the chit-chat through the afternoon matinee and you might get shushed.
Oddly enough, converse was originally a verb meaning “to move about, live or dwell” when it first came into existence in the mid 14th century. But today we only use converse to talk about, well, talking. Quipped the German philosopher Friedrich Nietzsche, “When marrying, one should ask oneself this question: Do you believe that you will be able to converse well with this woman into your old age?” A good question for marrying men and women!