Once the Moz Access ID and Secret Key are provided, we start retrieving back links for each of the competitors you associate in the system and pool that data along with our own back link sources, remove duplicates, crawl the anchor text and present you a much more comprehensive list.
In addition, within Page Clarity Detail you should see a few new columns show up where Partner URL's (back links) for competitors are displayed - mozRank and PageAuthority. This helps provide additional data points when choosing which specific links to pursue from your competitor's back links profile.