Domain Authority is a metric that Google and other search engines use to rank webpages. Sites with a high Domain Authority will achieve a higher SERP ranking than those with low Domain Authority. The sites with the highest Domain Authority tend to have a large number of relevant outside links as well as a large number of relevant sites linking to them (i.e. backlinks). You can check your backlinks and their quality using LXRMarketplace's Inbound Link Checker tool.