In the SEO sense, an authoritative site is a website that has unique content, inbound links, outbound links and is highly rated by search engines.   When seeking to build your external link inventory, your site can receive more benefit by being linked to from an authoritative site that is relevant.  Authority sites tend to be more trusted and have a higher Page Rank.  A site with a Page Rank 7 would be considered more of an authority by Google than a site with a Page Rank 3.