PageRank is the algorithm Google was founded on: a page's importance is estimated from the number and importance of the pages linking to it. Google still lists link analysis systems and PageRank among the systems it uses today. The public score was retired years ago, but the principle that links from trusted pages confer trust has never gone away.
The idea in one paragraph
Imagine someone clicking links at random around the web forever. Pages they land on often are important; pages they rarely reach are not. A link from an important page is worth more than a link from an obscure one, and a page that links out to hundreds of things passes less to each than a page that links to three. That is PageRank, published by Google's founders in 1998, and it was the first ranking method that could not be beaten simply by repeating a word.
What changed
The number itself disappeared from view. Google removed the public PageRank score from its toolbar in 2016 after years of not updating it, mostly because people were buying and selling links to move it. Inside Google it carried on as one signal among many, refined so that links are weighted by where they sit on a page and whether anyone is likely to click them.
Google's current guide to its ranking systems still names link analysis systems and PageRank, alongside systems that understand language, freshness, originality and spam. Links are no longer the whole story. They remain part of it.
Why it matters to a small site
Because it explains the things that otherwise look random. Pages get indexed faster when something links to them. New sites struggle for months and then loosen up. A page nobody links to sits still no matter how many times it is edited. All of that is links doing what PageRank says links do.
It also explains the shape of the fix. You cannot buy your way out without breaking Google's link spam rules, but you can earn links from suppliers, partners, local organisations and press, and you can route the authority you already have around your own site with internal links.
What not to conclude from it
Not that domain-level authority scores from SEO tools are PageRank. They are estimates built from crawls of the link graph and Google has said it does not use them. And not that links alone will rank a page that does not answer the query. Relevance is judged separately, and a strong page on the wrong topic ranks for the wrong topic.
Sources
Where this shows up in the tracker
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Related terms
Backlink
A backlink is a link from someone else's website to a page on yours. Search engines treat it as a vote: the more trusted and relevant the site casting it, the more it counts. Links are still among the strongest ranking signals Google has, which is exactly why buying them is against Google's rules and why earning them is slow.
Domain rank
Domain authority, domain rating and domain rank are scores from zero to a hundred that SEO tools calculate from the links pointing at a website. Each tool has its own name and its own formula. Google has said repeatedly that it does not use any of them. They are useful for comparing sites against each other, and useless as a target in themselves.
Internal linking
Internal linking is linking from one page on your website to another. It is how Google discovers most of your pages, how it works out which ones you consider important, and how it learns what each page is about from the words used to link to it. It is also the one ranking lever that costs nothing and that you control completely.
Anchor text
Anchor text is the visible, clickable words of a link. Search engines read it as a description of the page being linked to, which makes it one of the clearest signals of what a page is about. Descriptive anchor text helps. Identical, keyword-stuffed anchor text across many links is one of the recognised marks of bought links.