The narrator, Jake Barnes, describes Robert Cohn, who was a middleweight boxing champion in college at Princeton University. Born into an old, rich Jewish family, Cohn had an easy childhood. But at Princeton he was made to feel like an outsider because he was Jewish. He took up boxing in response to his resulting feelings of inferiority. He liked knowing he could knock down anyone being nasty to him, though he never actually fought anyone outside the gym.
Jake introduces Cohn first and puts himself in the background, setting the pattern of Jake trying to avoid his own story. Note how Cohn responds to feelings of insecurity by finding refuge in sports, but also how he is too honorable to every actually use those skills outside the sporting arena. Note also that Cohn's past does not include fighting in WWI.
Jake comments that he naturally distrusts anyone who seems as simple and honest as Cohn, but after some checking around he did verify that Cohn was in fact what he said he was.
That Jake mistrusts simplicity and honesty suggests the depths of Jake's skepticism of everything, and also suggests that he himself is not being entirely honest about himself.
Cohn emerged from college shy and self-conscious, and quickly married the first girl who was nice to him. He had three children in five unhappy years during which he lost much of a fifty-thousand dollar inheritance left to him by his father. Finally, just as Cohn was deciding to leave his wife, she left him for another man.
Cohn married not for love, but rather on the rebound from a tough college experience. Note that Cohn did the traditional thing upon leaving college: he got married. He also then tried to do the honorable thing in resisting leaving his wife for as long as he did. Both following tradition and being honorable ended up badly for him.
Cohn moved to California after the divorce. He fell in with a literary crowd and began to fund an art magazine, and soon made himself its editor. Meanwhile, he was "taken in hand" by a woman named Frances, whom he thought he loved, but who hoped to climb the social ladder as the magazine became better known.
Cohn assumes that being in a relationship with someone must mean you love them. He's deluded by tradition and romantic ideals of love. Frances isn't—she's in it to get something for herself.
When the magazine failed, Frances decided to get what she could from Cohn, and got him to take her to Europe. They settled in Paris. Cohn lives on an allowance from his mother and has two friends: Braddock, his literary friend, and Jake, with whom he plays tennis. Cohn is "fairly happy," except that like many other people in Europe he would rather be living in America. He writes a novel and fills his days reading, playing cards and tennis, and boxing.
Frances continues to use Cohn. Europe was supposed to provide an artistic escape, but none of the Americans actually seem to like being there. Yet for some reason they can't seem to return to America either. They're lost, unable to escape and unable to find home. The male relationships are defined by activities with competition at their heart.
At this same time, Frances realizes that she's losing her good looks and shifts from treating Cohn carelessly to trying to get him to marry her. Jake notices this change in Frances when, one night, Jake, Cohn, and Frances go out to dinner together. Cohn suggests he and Jake take a trip to get out of Paris and do some hiking. Jake says he knows a girl in Strasbourg who can show them around, but gets a few kicks under the table from Cohn and an angry look from Frances before he realizes his error.
Frances's desire for marriage is purely practical and self-serving. The men of the novel often seem to be at the mercy of the women, and the desire to take a trip into the countryside, into nature, is in some ways a desire to escape from women (who in the novel tend to stay in the city). The desire for change purely for itself also characterizes the Lost Generation.
Later, Cohn walks Jake out of the café and scolds Jake for making Frances jealous. Any mention of any girl will set off Frances, Cohn says, to Jake's disbelief. Cohn then worries that Jake is "sore" with him, but Jake assures him he isn't. They decide to go to Senlis instead of Strasbourg. Despite all the silly drama, Jake comments that he likes Cohn.
Jake's relentless interest in Cohn shows us that Cohn is an important mirror through which we come to know Jake. He is competitive and literary but also very different because he was not in the war.