I saw the movie before I read the book, and I am honestly not sure whether that was a good or bad thing. I loved the movie, and I loved the book, but they are very different.
Generally, the book is a very fast-paced and interesting read about the black women who worked at the Langley Air Force Base in Hampton, Virginia, and their many and varied contributions to the field of aeronautical and astronautical research. It is part biography, part history of NASA, part history of segregation, part history of the civil rights movement, part history of the Virginia peninsula, and part history of women's rights. It is absolutely fascinating.
That being said, the book is very different from the movie, so don't go into it expecting them to be the same. The movie is deeply touching, but it is actually fairly inaccurate, and it has been pretty aggressively whitewashed (see re: the Kevin Costner character). I think it is good to both see the movie and read the book, because one of the critical differences, and the difference that I think is missed entirely by the movie (to its great detriment) is the way in which issues of segregation were actually tackled at Langley. The movie makes it appear that enlightened white men of power were responsible for Langley's integration, when in fact the integration of Langley was almost entirely borne organically and of necessity. The book does a good job of explaining this, whereas that aspect of the movie is almost entirely fictionalized. I thought the movie took away some of the women's victories in this area (Katherine Johnson, for example, never went to the "colored" bathroom. She just used the regular, unlabeled bathroom, and no one ever told her not to), but the book gives the women more credit for their small yet trailblazing acts of defiance.
One other note: the book actually covers quite a bit of complex scientific detail, but it is entirely readable to the layperson.