What is Authority Links?
Authority links are links from websites that have established a substantial degree of trust and authority with search engines as a result of their age, quality, and size.
An authority link is a backlink from a site already trusted by Google or Bing or Yahoo. That means that most people visiting the site - trust the info on said site.
Authority links are from sites that essentially have "authority" for example google places, bing business, yelp, and a lot of the other directories. It also includes local directory sites like the BBB or chamber of commerce. The thing to remember is not all sites have the same authority because it's related to their page rank, domain age, backlinks pointing to their domain, etc.