I did not view Firefly until about three years ago. So I'm coming at this after also watching Serenity... and I think I've a fuller picture than ray gower and the other posters from 2001.
For me, Derrial Book is the conscience of the crew. He is quick to defend and quick to give grace... while never compromising his faith. I'm not saying Mal does not have a conscience, just that Book is the resource for Mal to turn to when he's undecided. He plays the role of father, mentor, uncle, grandfather, and friend. Not everyone gains wisdom with age and perhaps Book is not the wisest, but he's patient... and the answers come eventually.
After seeing Serenity, I think it's a given that Book was some sort of Fed insider. This is obvious from Bushwacked, but the movie shows us The Operative's life, motives, and crossroads... and it's an easy stretch to apply that Book.
I imagine that Book was some sort of agent. I think he was sent on a long term mission. I think he did something and/or saw something that changed his outlook. I think he never went back and told his superiors of his change of heart. I think Book just joined a monastery... and his superiors assumed he was taking a different tack, but was still on the case. They had to assume this because of his priority status in Bushwacked. But somewhere along the line his superiors realized he was not helping them with either the Tams, his original mission, or by resisting Federal plans for Haven.... and I think his superiors disavowed him or actively made him a target for The Operative.
Book is obviously committed to serving as a Shepherd. His faith is genuine. Inara knew every time people tried to manipulate her and she resisted it... but she takes to Book at the end of the pilot because his concern was genuine.
I think he was determined to serve God as an agent against the Feds... and his breakdown in front of Inara stemmed from two factors... First, he did not find an easy flock to shepherd. Maybe he was thinking to really be a pastor... Second, he fell in with people who also were anti-Alliance and could assist him in his long term ideals... but staying with them would put him on the Alliance's radar very quickly and shorten his life considerably.
And Book had to make his decision... and he stayed with Serenity and shepherded the crew as they defied the Alliance. His conscience ruled him.
At the beginning, Mal was openly hostile to Book. But by the movie, Mal trusted Book as much or more as he trusted Zoe. Conscience. Wisdom. Patience. Helping people. Building a good community. Mal came to respect Book's works because they were the same as Mal's.
I loved the way that Book refused to tell Mal of his past. The past, while interesting to us, no longer interested Book. He lived for the now... and for other people's futures. He lived according to his conscience... he did not live in the past... he did not live with regret anymore. But Mal knew that Book had a past that involved secrecy and violence for the Alliance... and he wanted an answer. By not telling Mal, Book was modeling how to live in the now... to live for the future. Mal had been living in the now with tremendous regret. Book was trying to set Mal free to hope, to love...