The story
From all-in-one (“combining two or more items or features in one unit”, adjective) + diaper (“an absorbent garment worn for incontinence”), so-called because this type of cloth diaper consists of both an outer, waterproof layer and inner, absorbent layer—whereas most other diapers did not contain a waterproof outer layer.
Etymology from Wiktionary, CC BY-SA 4.0.