Authority refers to the credibility of the source's author.
Ask yourself these questions when thinking about the authority, or credibility, of a source and its author/publisher:
This information is often given in a section labeled “About." If you’ve arrived in the middle of a web site, you may need to make your way to the main page of the author/sponsor to find this information
Are you using information for a research assignment? For example, if you are researching about the importance of bilingual education, you would want to use sources written by experts in the educational fields. Likewise, if you were searching for information about how to fix your vehicle, you might consult a local mechanic because he or she is knowledgeable about cars.
For example, you might use Yelp to read reviews of restaurants in your area. In this case, it doesn't matter if the reviews at Yelp are written by average people who are not "experts" in the restaurant industry.
Image Source: Aufsicht einer am Laptop arbeitenden Frau by Marco Verch Public Domain
(Thank you to Tacoma Community College https://tacomacc.libguides.com/c.php?g=373171&p=2522785)