i think its something like reputation. Like what reputation you have in world. Are you an professional who is usefull to others and you are well known? Than maybe you have good authority. Similar can be in domains world..? Your site is frequently and constantly mentioned and liked on social networks and other sites.
Domain Authority metrics are part of many of SEO and online marketing platforms and it can be measured using Open Site Explorer and MozBar. It's important to know that it's hard to influence it directly. The best way to influence it is to improve SEO.
Get A Cheap Windows VPS/RDP at CheapWindowsVPS.com
Domain authority is a moz rank tool to rank a website based on its back links. DA is not considered by some webmaster for having good rank and traffic.