To get along well (with someone). To hit has long meant, in a secondary sense, to succeed, probably from a sport or game. Shakespeare used it in this way in numerous plays; for example, “Have all his ventures fail’d? What, not one hit?” appears in The Merchant of Venice (3.2). To “hit it off ” seems to be an elaboration of the same meaning, and dates back to the eighteenth century. “How do you and the great Mrs. Montague hit it off,” wrote diarist Madame d’Arblay in 1780.