What Domain Authority actually is
Domain Authority (DA) is a metric invented and owned by Moz, a search-marketing software company. It predicts how likely a domain is to rank compared with other domains, based mostly on the quantity and quality of links pointing at it. Ahrefs has an equivalent called Domain Rating and Semrush has Authority Score — the three are calculated differently and are not interchangeable.
The most important fact about Domain Authority: Google does not use it. It is a third-party estimate, useful for comparing yourself against competitors, not a score Google awards or reads. A local business can and regularly does outrank higher-DA competitors on searches where relevance, proximity and reviews matter more than links.