"Until a man is twenty-five, he still thinks, every so often, that under the right circumstances he could be the baddest motherfucker in the world. If I moved to a martial-arts monastery in China and studied real hard for ten years. If my family was wiped out by Columbian drug dealers and I swore myself to revenge. If I got a fatal disease, had one year to live, devoted it to wiping out street crime. If I just dropped out and devoted my life to being bad."
-Neal Stephenson, "Snow Crash"
Batman is a higher state of being particular to fictional worlds. In any given universe, the Batman is that world's biggest bad-ass. This bad-ass is represented numerous ways- strength, toughness, genius, etc. This accompanies strong, authoritarian personalities and immense will.
Though they are not usually the most powerful person in their worlds, they are most certainly the Winners. It is nearly impossible to stop one who has attained Batman. Their will to survive/fight/win is simply too strong.
They're known for taking things "too far". This is quite simply because attaining Batman requires that you're more than a little crazy. Sane people simply would not do the things Batman does. Batman even scares the other good guys.
Well known examples of the Batman state: Jack Bauer, "24"; Jack Bristow, "Alias"; John McClane in later "Die Hard" films; Harry Calahan, "Dirty Harry" etc; El Mariachi, "Desperado" etc;