PageRank
In plain terms
Google's original algorithm for ranking web pages by importance.
Going deeper
PageRank scores a page by the quantity and quality of pages linking to it, modeling a random web surfer's long-run visit probability. Important pages confer more rank.
Under the hood
Computed via iterative matrix multiplication (power iteration) with a damping factor; a foundational link-analysis method.
Examples
Search ranking, citation analysis, influence in social networks, recommendation.
Think of it like...
Like ranking people's influence by who, and how influential the people are, that vouch for them.