It is derived from the Sanskrit verbal root nand, which means "to rejoice, delight".
Literally, nandinī means a woman who brings joy.
In the Hindu religion, Goddess Parvati is often addressed by this name.
Nandini also refers to one of the eight eternal companions (Ashtanayika) of Goddess Parvati.
This may point towards Bill Withers' fascination with the Indian subcontinent and his study of the Sanskrit Language.