PageRank
PageRank is the algorithm developed by Larry Page and Sergey Brin at Stanford University that rates the importance of a web page by the number and quality of incoming links: links from important pages count for more than links from unimportant ones. It was the original core of Google's ranking system – the underlying patent US 6,285,999 B1 was filed in 1998 and granted in 2001 – and is still regarded as the conceptual basis for evaluating websites through backlinks.
In practice
Google retired the publicly visible PageRank toolbar display in 2016, because it had encouraged manipulative link building purely to raise that figure. Internally, Google still uses PageRank-like signals as one of many hundred ranking factors, combined with quality and relevance signals such as E-E-A-T. In practice that means systematically building high-quality, topically relevant backlinks remains important, but treating "optimising PageRank" as a metric of its own no longer makes sense, since no public tool reports it any more.