Website authority" is an SEO concept that refers to the "strength" of a given domain.
Some people call this "domain authority," which is not to be confused with the Domain Authority (DA) metric from Moz. When we talk about domain authority, we're talking about a general SEO concept that's synonymous with "website authority".
Here at Ahrefs, we have a website authority metric of our own called Domain Rating. It runs on a scale from zero to a hundred. The higher a website's Domain Rating (DR), the stronger and more authoritative it is.
The free tool above shows your website's "authority" as calculated by Ahrefs (i.e., Domain Rating).