Website authority
Website authority is an SEO tool's estimate of how strong a whole site is, mostly from the links pointing to it.
Website authority is a score that estimates how strong a whole website is, mostly from the number and quality of links pointing to it. It isn't one standard metric. Each SEO tool has its own: Ahrefs has Domain Rating, Moz has Domain Authority, and others use their own names. People say website authority when they mean any of them.
Marketers use it to size up sites quickly. Is this blog worth pitching? Is this directory worth being listed in? Is a competitor's site much stronger than ours?
What the score can and can't tell you
Each tool works out its score from its own crawl of the web, so the same site gets different numbers in different tools. None of them is a Google number.
A high score means a site is well linked, which usually means it's well known and well read. It doesn't mean the site is trusted on your subject, or that it ranks for the searches you care about.
For example, a national news site might score 90, and a specialist coffee review site 40. When someone searches for the best burr grinder, the review site may well be the one that ranks and gets read.
Authority in AI search
AI platforms decide which sources to use in their own ways, and they don't publish a score. What you can see is which sites they actually cite for your questions. Often those include well-known sites, but also specialist blogs, forums and review sites that an authority score would rank low.
So use authority scores to sort a long list of sites, then check which of them the answers in your category actually use before you put time into them.
In AnswerOrbit
Sources shows which domains the answers to your prompts used, how often, and on which platforms. The Gaps tab scores each source out of 100, half by how often answers use it and half by how many of your competitors it names, which tells you where a mention would count.