Search visibility is measured with a lot of numbers, and only some of them mean anything. This site explains the metrics that appear in common SEO tools, what each one is actually derived from, and how much weight a working site owner should give them.
Start with the distinction between a metric a search engine publishes and a metric a tool invents. Search engines expose very little: whether a page is indexed, roughly which queries it appears for, and how often it is clicked. Everything else, including the widely quoted authority scores, is a third party estimate built from a crawl of the public web. Those estimates are useful for comparing two pages, and misleading when treated as a score a search engine holds.
Link metrics are the clearest example. A tool counts the pages it has crawled that link to a target, weights them by its own estimate of each linking page, and compresses the result onto a convenient scale. Two tools will disagree about the same site because they crawled different portions of the web. The number is a relative signal, so it is worth watching direction over months rather than reading a single value as a verdict.
Keyword difficulty behaves the same way. It usually blends the link metrics of the pages currently ranking with some measure of how commercial the query looks. It cannot see how well those pages actually answer the question, which is why a thoroughly written page sometimes ranks against apparently stronger competitors, and why a thin page on a strong site sometimes does not rank at all.
The metrics genuinely worth tracking are less exciting. Whether important pages are indexed at all. Whether they load quickly enough that a visitor stays. Whether the title and description accurately describe the page, because those decide the click. Whether internal links make an important page reachable in a couple of steps from the home page. Each of these is directly actionable, which is exactly what an authority score is not.
Crawl data is the other half of the picture. A crawl of a site finds broken links, redirect chains, pages excluded by directives nobody intended, duplicate titles, and pages that exist but appear in no sitemap and no menu. These are unambiguous defects with unambiguous fixes, and they are usually worth more than any amount of work aimed at moving an estimated score.
Measure a few things that connect to a decision, record them on a schedule, and treat every third party number as an estimate with a margin of error. That approach is duller than chasing a score, and it produces better decisions over a year.
It is worth being explicit about what none of these numbers can tell you. They cannot say whether a page answers the question a visitor arrived with, whether the writing is trustworthy, or whether a reader who lands on it will come back. Those are the things that decide whether a site is worth ranking, and they are assessed by reading the page rather than by querying a tool. The reasonable use of measurement is to find pages that are broken, slow, unreachable or misdescribed, fix those, and then spend the remaining effort on the content itself. A dashboard is a way of finding work; it is not a substitute for having done any.