The series is set in an AU from the movie, and focuses on Major Kusanagi and the Section 9 forces in future-noir adventures and mysteries. For those clueless about GITS, it's set in the near future where most people have traded in parts of their bodies, whether by choice or necessity, for cybernetic parts, and centers around Major Motoko Kusanagi, who became a full cyborg as a child(I forget if it was an accident or an illness) who heads up Section 9, a law enforcement unit composed of other cyborgs(with one exception) She's one of the(if not the) strongest and most capable anime heroines out there and, though she claims to have no nostalgic attachment to humanity, clings to it more than she'd admit(and more than even Batou would call her on)
My favorite characters are Togusa, the sole member of the group whose body is entirely human aside from certain required cyber netics, and Batou, the Major's friend/confidant/enforcer. Togusa is different from most anime characters in that he's a family man...happily married with 2 kids and a nice suburban house. He's the only remotely normal member of Section 9, and also the youngest. That and his tendency to go around trying to be a hero tends to get him teased a lot, especially by the Major(one of her few examples of humor.) Batou is ex-everything covert and seems to take things lightly but is actually pretty serious and more than a bit of a mother hen.
The series is one of those that people talk about when they say none of the good anime ever gets released in the US, just the kiddy and fanservice-y stuff. Except, you know, it has been licensed and released. It's flat out one of the best animes to make it stateside, and also has some of the best animation(that almost completely avoids most of the normal anime animation themes) and one of the best soundtracks.
BTW, while i like the movie, I far prefer the series.