The first book is about a girl named Lyra whose best friend is abducted (along with lots of other poor children), and, when she discovers that her mother is one of the operation's ringleaders, joins an effort to rescue him/them. It's a fairly straightforward tale, albeit with a memorable detour into a political fight amongst armored polar bears, but the movie was in such a rush to hit the bullet points of the story that her friend and his importance to the narrative, while present, were drastically under-emphasized.
The book then ends with a sharp and dark twist, to which Lyra's friend is also crucial, but the movie omitted this (filmed and finished!) sequence out of cowardice, so, if you haven't finished the book and have only seen the movie, you wouldn't know that, and since the friend only appears at the beginning and conclusion of the story, to lose the ending is to lose that key bookend element that ties the narrative together.
The next two books are a bit more open-ended, in that Lyra doesn't always have such a clear overarching goal; they're more about her evolving into womanhood, with plenty more adventures along the way. And, as theenglish says, organized religion plays a central villainous role. To say more would be spoilery, but that's the trilogy in a nutshell.
