The films omit a number of major episodes which are in the books, and also have composite characters. As with any book, a movie version can "fit in" a lot less than the book can.
The other major difference you'll see is the "The Two Towers" and "The Return of the King" each have a number of different viewpoints, with story strands which overlap in time. This greatly increases the suspense compared with the "linearised" timeline of the films.
The books are just so much better in every way.