In The Dark Knight, Alfred tells a story of a bandit to Bruce which draws parallels to the Joker himself. But what is the significance of this story? And how does it help him deal with the Joker?
The significance of the story is basically to tell Bruce (and the audience) something he can't understand, namely that the Joker isn't to be understood, reasoned with or bargained with. The primary purpose of the story is just to reinforce the Joker's characterization as someone who doesn't strive for any "worldly" or reasonable goal, rather than just sheer chaos. It thus adds into the many other allusions to his random and chaotic personality throughout the movie, from the money burning to the various different scar stories and general lack of a backstory.
While Bruce, the ever clever detective, tries to understand what drives the Joker and what his plan is, Alfred with his experience has realized (or at least considers the option) that there might not be any plan behind the Joker's actions, or at least not any monetary or otherwise reasonable end goal.
I'm not sure the story's purpose ever was to directly help Batman deal with the Joker, but if anything, it told him what he has to deal with really (even if he might not have believed it at that point yet). He realized that he is basically fighting a terrorist without any worldly goal. So the only way to stop him is practically burn down the forest, and that is what Batman actually does at the end.
When he activates the cell-phone radar he basically sees the entire city and there is no way for the Joker to hide anymore, he burned down the whole jungle this city is. But the jungle analogy also adds to the darker side of this idea, since not only does he see where the Joker is, he also sacrificies the privacy of all of Gotham's citizens and thus part of his integrity as a guardian of those citizens. In the same way burning down a jungle for just one bandit isn't really a good thing, it's a desperate measure against an uncontrollable enemy. But in contrast to the jungle, Bruce has the option to just restore it as it was, and he is considerate enough to do so at the end of the film.
I always thought it was Alfred saying that sometimes people don't have a grand idea that they are working for, a reason upon which their deeds can be "excused". Some people just "like to see the world burn", they do evil for evil's sake.
In this respect it allows Bruce to see that people like this, like The Joker cannot be reasoned with, as there is nothing they want other than destruction and mayhem.
I believe this would allow Bruce to deal with The Joker knowing that the only way to deal with him is to stop him, and to not try to reason with him.