What is the appeal to authority fallacy (ad verecundiam), and when is citing an authority not fallacious?

Treating a claim as true just because an "authority" said so — fallacious when the person isn't a legitimate, unbiased expert on that actual subject.

Citing experts is often perfectly reasonable; we can't verify everything ourselves. It becomes the fallacious appeal to authority when one or more conditions fail. The widely-used checklist:

1. The person has genuine expertise in the subject.
2. The claim is within their area of expertise (a brilliant physicist is not thereby an expert on nutrition or politics).
3. There's broad agreement among experts (in genuinely disputed fields, each side can cite its own experts, so the appeal settles nothing).
4. The expert isn't significantly biased (e.g. paid by a party with a stake).
5. The field is a legitimate one (not, say, "master psychic").
6. The authority is actually identified — "scientists say…" with no named source can't be checked.

"This actor endorses the supplement, and he's famous, so it must work."

Fame isn't medical expertise. Even a good appeal to authority is relatively weak — direct evidence about the claim itself is always stronger.