As the previous definition of argumentation should make clear, it is impossible to make an argument without first holding some premise in common. Since most premises are supplied by authority, arguments almost invariably rely on authorities held in common.
Appeals to authority are valid insofar as we consider that authority to be a trustworthy or reliable source of evidence within a particular sphere. Stephen Hawking is a brilliant theoretical physicist and a nearly unimpeachable authority when it comes to his specialized field. In other fields, I do not think him as reliable an authority, as in questions of extraterrestrial life, alien invasion, and the existence of God.
The "appeal to authority fallacy" revolves around the a claim that a particular authority is infallible or beyond criticism in a certain field. Such claims are generally reckless, and unworthy of consideration, except where the claim of authority intrinsically entails such infallibility.
For instance, Scripture claims to convey the words of Christ and of God, transcribed by human agents who were themselves acting under divine inspiration. If these words were anything less than perfectly True, Good, and Beautiful, Scripture would lose its value as an authority. Therefore, the Scriptural claim to infallibility is intrinsic to itself and must be treated separately.
It may be noted that the question of Scriptural infallibility faces the same trichotomy that C.S. Lewis ascribed to the divinity of Christ, the famous "Lord, Liar, or Lunatic" argument. Either Scripture is divinely inspired and thereby infallible, or it's a deliberate lie, or it is a simple exercise in authorial delusions of grandeur.