The PageRank algorithm, created by Larry Page and Sergey Brin in 1996, ranks websites by setting up and solving a large system of linear equations that represent how pages link to each other. Each equation balances the importance of a page with the pages that link to it, using basic ideas like variables and weighted sums. This ranking helps search engines decide which websites appear first in search results, making it one of the most important tools for finding reliable information on the internet.