A plain-language explanation
PageRank is a system developed by Google for assessing the importance of pages based on the network of links leading to them and the value transferred between documents.
Where it helps in practice
PageRank describes a historic and conceptual link-graph method, while the old public toolbar score is no longer a current SEO measure.
The decision before implementation
Focus on logical connections, source quality and page accessibility rather than searching for one PageRank number.
How to verify the result
Assess crawl, links, visibility and traffic while separating algorithm theory from present-day reporting.