Throughout The Catcher in the Rye, Holden mentions his desire to give Jane Gallagher a call. In fact, his fight with Stradlater occurs because he's afraid that his roommate gave Jane "the time" in the back of Ed Banky's car without really caring about the girl.
Jane's one feature that Holden obsesses over is her habit of keeping all of her "kings in the back row" when playing checkers. He says that she doesn't do this for strategy or anything, but because she "liked the way they looked." Because Stradlater is incapable of recognizing this girl's unique habit, Holden loses his mind and attacks his roommate, repeatedly calling him a "stupid moron" who "didn't even care if a girl kept all her kings in the back row or not." Then Holden tells Stradlater that he can't see a girl for who she is and that he doesn't "even know if her first name is Jane or Jean, ya goddam moron!"
But there is a lot more to Jane than her checkers habit. According to Holden, Jane was very athletic and they played tennis almost every afternoon. In addition, Jane was someone Holden says was different, but whom he liked a lot. In fact, Holden respects Jane so much, she's the only one he shows Allie's glove to.
Here are a few longer quotes that show his feelings toward her:
"I wouldn't describe her as strictly beautiful. She knocked me out, though. She was sort of muckle-mouthed. I mean when she was talking and she got excited about something, her mouth sort of went in about fifty directions, her lips and all."
"Most girls if you hold hands with them, their goddam hand dies on you, or else they think they have to keep moving their hand all the time, as if they were afraid they'd bore you or something. Jane was different. We'd get into a goddam movie or something, and right away we'd start holding hands, and we wouldn't quit till the movie was over. And without changing the position or making a big deal out of it."