PageRank is one of many methods for ranking the value of a web page.
PageRank is a Stanford University patented algorithm for determining the relative value of individual documents from within a group of linked documents. PageRank is named for Larry Page, one of Google's founders. PageRank is used exclusively by the Google search engine as part of how they sort web pages in their search results.
PageRank is an important term in SEO (Search Engine Optimization).
PageRank is one method of weighing and valuing internal links and external links to your web site, and then applying that value to your own site.
Since Google has exclusive rights to the algorithm and to use the term in relation to their search results, your PageRank is only relevant to how your web site or web pages show up in Google's search results, but other search engines use similar processes to help provide quality search results to their users.