Domain Authority (DA) is a metric created by the SEO consulting and research company Moz which measures a website's likelihood to rank on search engines. "Authority" is often used outside of Moz's metric to describe a domain's relative "strength," determined in large part by their backlink portfolio.
Domain Authority is used as a predictive measure for PageRank, Google's proprietary algorithm that plays a major role in determining search engine results. Due to the shroud of secrecy around PageRank, Moz's DA metric is widely considered to be one of the best third party tools for evaluating domain strength.