A demon that can enter your dreams.. know your deepest desires... and worst fears. He uses that knowledge as he preys on you. Imagine not trying to sleep to avoid any contact with this person. Fighting the urge of slumber because you know not only will you experience the worst thing you can imagine, but also waking up dead.
Let's look at his resume. He killed the second Robin; raped and crippled Barbara Gordon (Batgirl and girlfriend of the first Robin. and he totured and abused Harley Quin; and the hundreds that he has terrorized and murdered. He is so evil that other criminals fear him.
The Joker is a character who is motivated by one goal in life: to corrupt the incorruptible. He is willing to shed as much blood, innocent or otherwise, in order to drive the Dark Knight into breaking is most sacred vow. The Joker only wants Batman to kill him because it means that even Batman can have "a bad day" just like him.