It's hinted at a few times in Firefly that Inara, like most of the crew, has an interesting past. Most notably, see the following conversation between Mal and Nandi in episode 13, "Heart of Gold":
NANDI: She ever tell you why she left Sihnon?
MAL: Never asked.
NANDI: Yes, you did. And I don't know, my own self. I was gone long before. And I'll tell you, it was a shock, her leaving. She was special. There's 40 women in House Madrassa and you'd pick her out in a second. Coulda been House Priestess, few years time.
MAL: Is that right?
NANDI: Had her eyes on it too. Very focused. She's like you, more than a little.
Shepherd Book's backstory has been revealed in other canon, so maybe the same goes for Inara?