Nolan's film delve into Wayne as a person, showing he is not just a vague secret identity. In "Batman Begins" you see Bruce as a child, experiencing happy, simple moments with his family rather than just reliving the murder of his parents. It shows his struggle to mentally come to terms with their deaths and his desire for justice. Batman is not just spawned right after his parents' death, but rather it shows the physical, mental, and emotional training he had to undergo to be an actual threat to the thugs of Gotham.
It shows how he plans his costume, where his gear comes from, why he chose the bat as his symbol. Batman battles not only the Scarecrow, but Ra's al Ghul, who actually mentored the caped crusader. Even during his training Bruce has his own code of conduct and will not kill, which demonstrates that you decide the life you are going to live by, not those who raise or mentor you.
"The Dark Knight"
"The Dark Knight" takes place awhile after the events of "Batman Begins" and the police along with Batman have been trying to clean up the streets and arresting the big mob bosses, which in turn causes the mob bosses to hire the up and coming Joker.
Wayne is confronted with a man who, as Alfred described him, "just wants to watch the world burn." The Joker has no past or weaknesses, he is chaos itself and Batman is mystified by his methods. He develops more of his detective skills in this film than in the previous one. He is also faced with the agonizing decision of not giving into the Joker's demands and making the impossible choice to act for the greater good.
As Alfred says, "Endure, Master Wayne. Take it. They'll hate you for it, but that's the point of Batman, he can be the outcast. He can make the choice that no on else can make, the right choice." (Side note Alfred Pennyworth has some of the best quotes throughout this trilogy)
"The Dark Knight Rises"
Batman takes the fall for Harvey Dent's actions as Two-Face and these events carry over into "The Dark Knight Rises" which is set 8 years after the Dent's death. Batman has gone into retirement and the police force has almost eradicated organized crime.
When the mercenary and mastermind Bane appears and successfully breaks Batman's back and holds Gotham hostage with a nuclear bomb, Wayne must retrain his mind and body while in the well-like prison that Bane came from. He comes to learn that fear of death is actually needed and that it sharpens his desire to live and save his city.
He displays his absolute devotion to Gotham by not only climbing out of the prison pit and duking it out with Bane, but carries a nuclear bomb out over the bay. Even though it is revealed at the end that he had an autopilot mode installed on the Bat, it is obvious to the viewers he would have done the same thing if he did not have autopilot. "Because he's not our hero. He's a silent guardian, a watchful protector. A dark knight," as Commissioner Gordon explained best.