In this answer, I will refer to Figure 1 in this link.
People who are in authority in an organization have the right and the duty to tell others what to do. This authority is shown by the vertical lines on the organizational chart. In this example, then, Tom Lee has the right and the duty to tell the managers under him what to do. He has no right to give orders to Juan Gomez or Pam Connors.
With authority comes responsibility and accountability. Lee is responsible for the actions of the managers underneath him. That means that what they do reflects on him. If they do badly for a long period of time, he may well be held accountable. This means that he could be punished for their mistakes. He is responsible for them, so he should have corrected those mistakes or found new managers who would not make those mistakes. Authority, then, gives the power to give orders, but it also makes those in authority responsible and accountable for the actions of those below them.