Domain Authority
Domain Authority is a third-party score, created by the SEO software company Moz, that estimates how likely a website is to rank in search results based mainly on the number and quality of sites linking to it. Similar scores include Ahrefs' Domain Rating.
What it is and is not
Domain Authority is not a Google metric, and Google does not use it. It is a useful comparison tool: if competitors have far stronger link profiles, ranking against them will take longer. But a high score does not guarantee rankings, and chasing the score for its own sake leads to bad decisions, such as buying links.

What actually builds authority
Links and mentions from relevant, trusted sites, earned through genuinely useful content, research, partnerships and PR. Google's spam policies explicitly prohibit link schemes and other manipulative tactics (Google Search spam policies).
How to use it
Use authority scores to compare yourself with the sites ranking for your target searches, and to judge which link opportunities are worth pursuing. Judge your SEO by traffic, leads and revenue, not the score. See SEO.