In the context of the topic website, the term authority stands for a website that has a high topic-specific relevance.
An authority therefore appears much more frequently in certain topic-relevant search queries than other websites. The high dominance in certain topics is due to a high link popularity with many inbound links. The more inbound links with corresponding relevance there are to a website, the higher its status is to be regarded, which is nothing other than authority.
An authority presupposes a high-quality content to which the backlinks refer. Authority does not come about with thematically irrelevant inbound links.