A stakeholder is a member of a group without whom the organization has no reason to exist. That word reason is key. Shareholders or the owners of a company are not the reason the company exists. At best they are a cause to bring it into existence, or to will its survival, but they had to have a reason to create the thing in the first place. The target of that reason, that's the stakeholder.
Never forget who the stakeholder is, because they dictate the nature of the work in the organization. The 1919 Chicago White Sox (forever now known as the Black Sox) forgot that the reason baseball organizations existed was for the fans and the nature of their work shifted from winning the World Series for those fans to throwing it to the Red Sox when they presumed three gamblers would make for a better stakeholder. They were wrong, by the way.
Schools have a stakeholder. Its the student that walks in the door. Remember that and the job is to maximize the educational benefit the school can provide given the unique needs of each child. But sometimes states think they should be the stakeholder, and if you believe that then the job of schooling is high or rising test scores regardless of student benefit. Those are two different jobs that are at odds with each other. And while I'm certainly not equating the state with a group of crooked gamblers, the effects on the organization called a school can be just as dramatic.