What story does Nick recall about Jordan, and what is the catalyst for his remembering?
I would like to elaborate on the previous excellent answer. At the house party nick discovers that Jordan can leave a convertible car in the rain with the top down and then lie about it, at which time he remembers that she had cheated at golf. Nick challenges Jordan that she is morally careless, which he sees embodied in her careless driving. “You’re a rotten driver,” he tells her (59). This becomes, of course, an important theme in the play in the relationship between Gatsby and Daisy and also foreshadows the accident later on. Jordan can take satisfaction in the fact that she is safe until she meets another careless driver, a charge she will bring against Nick at the end of the novel (179). Thus Jordan’s remark that she hates careless people, telling Nick “That’s why I like you” (59), seems ironic, as does Nick’s own claim that he is one of the “few honest people” he has ever known (60). In fact, no one in this novel is particularly honest. Nick’s growing entanglement with Jordan, therefore, parallels his telling of the Gatsby-Daisy story, and also raises questions at the outset about his own moral integrity.
At Gatsby's party in chapter three, Nick recalls that Jordan cheated in order to win her first golf tournament. He, however, dismisses this by saying (and I paraphrase) that dishonesty is not to be taken seriously among young women.
Nick remembers this - after some trying - because Tom and Daisy have been encouraging him to see Daisy. Nick knows that he must first break off a romance with a young woman back home, because he recognizes that this is the honest, appropriate thing to do - and Nick fancies himself an honest, upright gentleman. He talks about what he does during the day - mostly to convince Tom and Daisy that he not just a leisure man who attends parties - and he boasts of his honesty, calling himself the most honest person he has ever known. It is through this recollection that Nick recalls the golfing incident with Jordan.