It's simple. He appeals to that part of us that wants to see justice done and can relate to someone going out into their neighborhood/city/whatever and stopping threats with his bare hands. He has no fancy powers, but has an origin story rooted in a relatable tragedy. He throws on dark clothes, finds criminals, and beats the unholy hell out of evil people with his fists. It appeals to our base need to get back and punish the bad guy. Bats also happens to look cool doing it. The well developed rogues gallery, classic detective tropes mixed with some sci-fi, and supporting cast doesn't hurt.