Kilson was a former inmate of Arkham Asylum and an accomplice of the Joker . He was used to free Lau from jail.
The Dark Knight
Kilson was a delusional criminal who imagined hearing voices. For a time he was incarcerated in Arkham Asylum.
At some point after his release from Arkham, the Joker found Kilson, and offered to remove the voices, "replacing them with bright lights, like Christmas". The Joker made arrangements for Kilson to have a cell phone surgically implanted just under the skin on Kilson's abdomen.
Kilson was involved in the Joker's attack on Harvey Dent. After Batman was knocked out on the streets, Kilson touched his mask and was electrocuted. The Joker kicked Kilson and spat on him for getting electrocuted. After the GCPD rounded up the Joker and his thugs, Kilson was thrown into the Joker's cell in the MCU jail.
Kilson tried to tell the police that he was suffering from convulsions. The police didn't believe him until he collapsed, then they were forced to take him out of the cell to do CPR on him, only to discover a long scar and a strange contusion on his stomach. The Joker took Gerard Stephens hostage, and demanded his one phone call. Murphy threw his cell phone to the Joker, who called the phone inplanted in Kilson.
A detonation device attached to the phone was set off in a powerful explosion, tearing Kilson apart. Kilson's unknowing assistance in the Joker's escape from the jail allowed him to free Lau.
Going by his statement about the Joker getting rid of the voices in his head and replacing them with lights, like Christmas, it can be assumed that he has Schizophrenia or some sort of manic disorder.
Behind the scenes
Credited as "Fat Thug".
Identified as Kilson in The Dark Knight's novelization.