There were four Horizon Story Businesses in the vanilla game initially. These are: Stunt Driver, LaRacer@Horizon, World's Fastest Rentals and the Drift Club. In addition, Businesses that were added after launch, like Isha's Taxis and Skill Streak also give progress towards this achievement. They can be easily found on the map, by setting the respective filter on.
Each chapter puts you in control of a certain car and you're tasked to complete an objective. Stunt Driver, which is unlocked from the beginning, requires you to make certain jumps, accumulate a certain amount of skill points, reach a point on the map quickly etc., usually in a spectacular fashion.
Each of the aforementioned event has 10 chapters, so you will need to finish four different Businesses of your choosing or mix it up. Getting three stars in all chapters though gives you the maximum weekly income from that Business, so it pays off in the long run to spend a little more time after unlocking this achievement to get all stars in all businesses.