The story
From the notion that the nappy is intended to last from around the baby's birth until they are potty-trained.
Etymology from Wiktionary, CC BY-SA 4.0.
birth-to-potty nappy
Today it means: Synonym of one-size diaper (“a type of cloth diaper which can be adjusted and lengthened to match the baby's growth, thus allowing the diaper to be worn from around birth (by a newborn) to potty-training age”). Full definition →