Figuratively, Allie's glove is a symbol for Holden's emotional expression. He keeps it hidden, it is precious and holds his heart. Allie's glove has poetry written on it. When Holden has to write a composition for Stradlater's homework, he looks to Allie's glove for inspiration. Allie's glove is Holden's connection to his feelings, which he reserves for a very few, Allie being one and Phoebe, his little sister, being the other.
It is connected to the story, because at the heart of the story is Holden's grief over his brother's death. Holden needs help dealing with this grief. He must take out the glove, literally and confront his pain and acknowledge his feelings in order to release himself from the terrible guilt and loss that he feels.
Holden does not understand why Allie who was much smarter than him died. He feels guilty that he, who lives because he is not sick like Allie was, is inferior and stupid. So it is the central emotion that dominates Holden's journey throughout the book.