What Page Authority measures
Moz maintains its own crawl of the web and its own record of which pages link to which. Page Authority is a model built on top of that record: Moz trains it against real search results, then outputs a score for every URL it knows, on a scale where the top is far harder to reach than the bottom. The heavier inputs are the number and quality of pages linking to that specific URL, so a page nobody links to scores poorly even on a well-known site.
Two things follow from it being a model rather than a measurement. It is a prediction of ranking ability, not a record of how a page has performed. And because it is scored relative to everything else in the index, it moves when the index is refreshed or the model is retrained, even if nothing about your page changed.
Why Page Authority matters
It brings the conversation down to the page, which is where ranking actually happens. A site can be widely known and still have a service page that no one has ever linked to. Comparing the Page Authority of your page against the pages currently ranking for the same query is a quick way to see whether you are short of links or short of something else entirely.
It is also a practical prompt for internal linking. When a page you want to rank scores far below the rest of your site, the cheapest fix is usually to link to it properly from pages that already have strength, rather than to go looking for new external coverage.
Where Page Authority goes wrong
People quote it as though Google reads it. Google does not. Moz built the score from its own index for its own customers, and no search engine consumes it. Anyone selling links on the strength of a Page Authority figure is selling their supplier’s opinion of a page.
The second problem is comparison across tools. Moz, Ahrefs and Majestic each crawl a different slice of the web and each weight links differently, so a page can look strong in one and ordinary in another. Pick one and stay with it; a number carried between tools means nothing.
The third is that the score is blind to intent. A page can be strongly linked and still lose to a weaker page that answers the query better, which is why link metrics should never be read without also reading the results themselves. Content quality and search intent decide more outcomes than link strength does on most keywords worth chasing.
How to act on it
Use it as a comparison, never as a target. Take the page you want to rank, take the pages beating it, and look at the gap. If the gap is small, the problem is probably the content, the title or the match to what the searcher wanted. If the gap is wide and consistent, links are the constraint and you have a case for link building work.
Then act on the page rather than the number. Point internal links at it with sensible wording, make it the destination in any coverage you earn, and give it a reason to be linked in the first place. The score follows the work; it does not cause it.