
Dexter was adopted at a young age under mysterious circumstances by Miami police detective Harry Morgan. Dexter is meant to be a sociopath, although he doesn't seem like most of the sociopaths we've ever seen, who mostly just go around forging signatures on cheques and ignoring people. After discovering him killing small animals, Harry does whatever any reasonable parent would do, and starts teaching his son to be a ninja.
As an adult, Dexter works as a blood-splatter analyst for the Miami police department with his adoptive sister, Debra. He uses his relatively privileged position to collect information on possible victims. At first Dexter claims to only go after victims who have 'slipped through the cracks' of the legal system, but later he appears to go after murderers who haven't yet been tried, presumably just for the hell of it.
Dexter also does a lot of stuff that is just super awesome, like knocking out a dude with a frying pan for insulting his girlfriend, and stabbing a pedophile. This allows viewers to experience such awesomeness vicariously, without having to go do it in real life and risk being brought down by The Man.
Well, maybe some Dexter fans also do it in real life. We don't know.
All summaries below contain SPOILERS.
Season One
Dexter is contacted via the bodies of dead hookers by a fellow serial killer, known as the Ice Truck Killer. Being the kind of dude that he is, Dexter is way into that. The series follows the police hunt for the killer and Dexter's developing relationship with his girlfriend Rita. Along the way, Dexter discovers that he became a sociopath for the medically dubious reason of witnessing his mother being killed in front of him with a chainsaw, which we admit, is probably a bit of a downer.
Season Two
The hidden bodies of Dexter's victims are discovered in an underwater trench off the coast of Miami. The series follows Dexter's attempts to avoid being uncovered by the investigation, and also his relationship problems with a creepy English chick. In the end, he deals with this problem in a way that is usually best when the English are involved, and kills her.
Season Three
Dexter navigates the obvious difficulties of being a serial killer who has also just impregnated his girlfriend. While not dealing with the vicissitudes of love, Dexter kills a few people. He also befriends Jimmy Smits, and then kills him.
Debra Morgan
Dexter's adoptive sister and a far more likeable and empathetic character, who is nonetheless given less sympathy from the writers since she isn't an interesting serial killer. She has particularly bad luck with men, since the man she dated throughout series one agreed with the writers and was basically just using her to get close to her brother.
Controversially, Debra eventually decided to deal with her man issues by marrying Dexter.
Sgt James Doakes
The only guy in Dexter's life who actually has any idea as to his real identity. He repeatedly refers to Dexter as a 'creepy motherfucker', insults him in front of others, and stalks him. Which, you know, Dexter actually kind of deserves.
Rita Bennett
Dexter's innocent and adorable girlfriend. Their relationship is a subject of deep identification with many Dexter fans, who think 'My girlfriend doesn't understand me sometimes either. It's kind of like being a serial killer," and then go and hang around in their deserted garages for a while, looking at gardening tools.

Just like you.
In Season Three Rita is revealed to have been hiding some secrets of her own. These include a previous short lived marriage, and also the fact that she is an immortal vampire.
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