Topical authority is the degree to which search engines treat your site as a credible, comprehensive source on a particular subject. You earn it by covering a topic thoroughly and accurately across many connected pages, rather than publishing scattered one-off articles.
There's no single "authority score," but engines infer it from patterns: how completely your content covers a subject and its subtopics, how clearly it connects related entities, the experience and expertise behind it (the substance of E-E-A-T), and how other credible sites and real users respond. A domain that answers the obvious question and the twelve follow-ups reads as authoritative; one thin post does not.
Depth beats breadth. Pick a subject you can genuinely own and cover it exhaustively with interlinked topic clusters, publish consistently, and make sure real expertise shows on the page. It's why a small personal-finance site devoted entirely to index-fund investing can outrank a large general-news outlet for those queries — it has demonstrated end-to-end command of one topic, while the bigger brand only grazes it.
Building topical authority is the long game behind any durable SEO strategy.