Batman is the introduction of the Dark Knight and The Joker into the world of prestigious cinema. On a deeper level, the film is about claiming one's identity and coming out of the shadows. For Bruce Wayne, he has been hiding in the shadows since his parents were killed in front of him as a little boy. So much so that he created an alternate personality in Batman to fight the killers that have plagued his heart and mind for decades. This is an origin story. We see that Batman directly affects the creation of the Joker and in turn we realize that The Joker created Batman. These two characters are on opposite sides of the same coin. One turned his rage into saving his city while the other chose to focus on destroying it.
With the entrance of Vicki Vale we see that both characters desire the same woman. Wayne falls in love with her which leads to the necessity to trust her more than anyone he's had in his life. This means that he will have to take off all of his masks in order to keep her love. For The Joker, his desiring of Vale is about further adding to the nature of the character. He does not seek to love Vicki, but to possess her. The Joker has no attachment to people as they are either useful or not, and Vicki is useful because he believes he is an artist and with her photography skills he will not only get to harness her beauty, but use her creativity to capture his "living art" as he destroys people's bodies and the city for his maniacal pleasure.
The final showdown between super-villain and superhero shows us that the two characters now know that they are created from each other's deep issues towards one another, and for us as the audience we watch as Batman comes face to face with the root of what has created him. And for the very first time he does what we have not seen him do: kill. Though The Joker falls to his death it occurs because of Batman's willingness to let him die. Symbolically, The Joker's death should put an end to Batman's search for peace. But, in the final shot we see that he is fully masked in his suit as he is more than a man after reveng, but a symbol of justice for all the people of Gotham.
