What is domain rating?
A domain rating is a metric developed to help predict how likely a domain, subdomain, or page will rank in search engine result pages (SERP). This website ranking measure is determined on a logarithmic scale, and the score ranges from 1 to 100, 1 being where all new websites start and move on from there.
Although we don't know the exact algorithm of Ahrefs' DR, it is calculated by looking at multiple Google ranking factors, including referring domain, linking domains, domain age, and the total number of links, into a single DR score. You might want to check Moz and its Mozbar if you use domain authority. The algorithm is different, but the purpose is the same: finding your website's authority and how it compares to competitors.
Whereas a website's domain rating measures the strength of a website, there is also a DR score attributed to each web page, called page authority or page rank.