Dexter is a forensic scientist ala CSI. Here is a pretty good explanation of the book it was based off (ripped from the offical site) but the series differes abit.
DEXTER is based on the compelling novel "Darkly Dreaming Dexter" by Jeff Lindsay, a South Florida native. Orphaned at the age of four and harboring a traumatic secret, Dexter is adopted by a police officer who recognizes Dexter's homicidal tendencies and guides his son to channel his gruesome passion for human vivisection in a constructive way - by killing those heinous perpetrators that are above the law or who have slipped through the cracks of justice. A respected member of the police force, a perfect gentleman and a man with a soft spot for children, it's hard not to like Dexter. Although his drive to kill is unflinching, he struggles to emulate normal emotions he doesn't feel, and to keep up his appearance as a caring, socially responsible human being.