The Joker was once a good husband to his wife and a good father to his unborn child, yet he could not find any job suitable for his comedic talent, preventing him from supporting his family.
As the situation becomes too dire for him to buy food, the man desperately work with the mobsters for the hope some money. On that fateful his wife and the unborn baby die horrifyingly in an accident, and the mobsters betray him when the chemical factory heist goes terribly wrong. At wit's end, he jumps into the poisonous river which changes his appearance forever, drives him crazy and marks the birth of the Man who Laughs. Tragedy is a man who can not weep for his loss.
This is how the concept of “One bad day” applies to Joker; however, Joker also uses this concept to challenge Batman’s sanity.
While Batman is considered a very rational detective, the Joker believes that Batman, in fact, is crazy. He tells Batman,
The two lunatics in the story who represent the Joker and Batman. Their escape from asylum illustrates the desire to be treated as normal human beings. But the gap between the buildings, the gateway between sane and insane worlds, prevents them from doing so.
The first lunatic overcomes this gap as the society somehow magically accepts that a man doing detective works in a "flying rat" costume is a pretty normal thing. Ironically, the very same society still treat Joker, a man wearing a clown make-up, as an outcast. The second lunatic is rational enough to recognize it, so he is hesitate to make a jump across the gap.
The first lunatic suggests he could use the power of enlightenment in the form of the flashlight to create a bridge to help his fellow lunatics make a leap of faith across that social gap. This is similar to how Batman offer the Joker help to rehabilitate in society, so that they will never end up killing each other.
The second lunatics again thinks rationally and rejects the leap of faith offer. No rational person will walk on a bridge created by light beam. It is rightly so for the second lunatic to call the first "crazy". Similarly, the Joker regards Batman's offer as crazy and unsustainable. Batman's "enlightenment" would collapse on Joker just like the first lunatics turn off the flashlight.