An authority site is more of a status you wish to achieve with your website as opposed to the site itself, however, the site has to support your goals. Think of an authority site as Wikipedia for a specific topic. For example, maybe you want to establish yourself as THE source for information on widgets (why is it always widgets?). To do this your site would need to contain lots and lots (and lots) of content about widgets. Top 10's, definitions, glossaries, video, links etc. As you can probably see this type of site is more about providing content. Once you have established yourself as an authority on a particular subject, you may wish to turn it into a membership site (see below).