The film begins with a young Bruce Wayne falling down a well and being terrorized by a swarm of bats. It ends with Bruce clothed as Batman as he begins to investigate The Joker. Between these scenes we see the journey of a young man who is enraged by the murder of his parents of by the justice system in Gotham having dismissed their duty to the people in order to accept the bribe money of the mob boss Falcone. Bruce wants justice and seeks to find it by murdering Falcone, something that he isn't able to do.
But the experience leads him to meet his mentor and teacher Ra's Al Ghul. A man who trains Bruce to harness the rage that is within himself in order to use it for a focused purpose. But he is not in alignment with Ra's who seeks to completely destroy Gotham rather than restore it. And Bruce learns that he is nothing like the man whom he admires greatly. This creates in him a rule not to kill, but to get justice without it. It is what separates him from everyone else who does crime in the city.
And Bruce's mask is about a couple of things. One, it is a symbol of hope for the people of Gotham that they can become the change they wish to see in their city, it isn't just one person's duty: it's all of theirs. The other symbol is that Bruce is more man than he is Batman. It is his love for Rachel and his desire to love and be loved that sets him apart from the vigilante role he's dubbed.
