The main point of the book was to establish the relationship between Galen Erso (Madds Mikkelson) and Orson Krennic (Ben Mendelson). Both met while students in "college". Krennic went on to be an engineer in the Republic military and Erso became a researcher. The novel starts during the Clone Wars. Erso is trying to create sustainable energy. He's a pacifist, so he's working on a neutral planet. Eventually, he and his pregnant wife get captured by the Separatists. Krennic organizes a rescue for Galen, his wife, and now baby daughter (Jyn). Erso has trouble finding work, and refuses to work for the military in any capacity, even after the war ends.
Krennic, meanwhile, is a Commander trying to advance his way up the Republic/Imperial military. His plan is to get the Death Star built, which he feels will get him promoted to Admiral. He makes some progress in getting the facility built, and develops a rivalry with Tarkin. When he hits a snag, he realizes that his old friend Erso is really the only scientist with the knowledge to create enough energy to make a weapon this big, however he knows Erso will never work for the military. He eventually gets Erso to work a special energy project for empire, under the guise that the project is to provide sustainable energy to underdeveloped planets.
Krennic is engaging is some black market arms deals that allows the Empire to pillage some natural resources from planets that were supposed to be ecologically protected. Galen's wife, who is a geologist, eventually uncovers this, and convinces Galen that his energy project is actually going to be used for a superweapon. While Krennic is busy trying to outscheme Tarkin, Galen, his wife, and his daughter escape to remote planet to hide from Krennic and the Empire. The novel ends with the Ersos living peacefully on this planet, and Krennic being demoted for losing Erso and putting the Death Star construction in jeopardy.
My guess is that the movie picks up with Krennic finding Galen and forcing him to renew his work.