Nandi was an old friend of Inara's and the madam of the Heart Of Gold brothel in the episode of the same name. Although she trained with Inara at House Madrassa to be a Companion, she left before she could complete her training because the life of a Companion didn't suit her. Inara explains on these grounds that she was a "whore", and not a Companion.
She was charismatic, and Mal's attraction to her (and sleeping with her) was painful to the otherwise serene Inara. This brought the feelings of the two for each other out in the open, and Objects in Space and future episodes might have gone further with that. Nandi herself died in the firefight with Ranse Burgess's men at the end of Heart of Gold.
Nandi was played by Melinda Clarke(approve sites).