In the hotel lobby, Holden thinks about the summer he spent with Jane Gallagher in Maine. Their families had rented neighboring houses, and Holden and Jane often played checkers and held hands.
Holden's memories of Jane are idealistic and un-sexual: they played checkers together and held hands.
Once Jane's stepfather made her cry simply by asking for cigarettes. Holden comforted and kissed her. He comments that when he would hold Jane's hand he would be truly happy, and adds that she was the only person he ever showed Allie's baseball mitt.
The reference to Allie's mitt connects Allie to Jane. Holden thinks of them both in pure, idealistic terms. Note how Holden enjoyed protecting and comforting Jane.
Now depressed, Holden remembers a bar called Ernie's that D.B. once took him to, and hails a cab.
That childhood dream is over. Reality depresses Holden.