Holden writes his composition for Stradlater about Allie's baseball glove. Allie was Holden's younger brother, who died of leukemia several years earlier, and the glove is one of Holden's most emotionally important memories of him.
The assignment comes from Ward Stradlater, Holden's roommate at Pencey Preparatory School. Stradlater asks Holden to write an English composition while he goes on a date with Jane Gallagher, a girl Holden knows and cares about. Holden deliberately focuses on the glove rather than producing the kind of ordinary descriptive essay Stradlater expects.
The glove is distinctive because Allie wrote poems in green ink on its fingers so he would have something to read while playing in the outfield. Holden's attachment to the object reveals how strongly he is still grieving. Stradlater's dismissal of the composition becomes one of the immediate causes of their violent confrontation, making the glove central to both the novel's emotional history and its plot.