Google pageRank
Named after one of Google's founders, Larry Page - not, as is widely assumed, because it relates to a specific web page (though in fact it is coincidentally based on the "ranking value" of an individual page) - Page Rank is one of many factors that goes into determining Google's SERPs rankings.
While it is true that Page Rank is not as important a factor as it has been in the past - and is most definitely not as important as a lot of second-rate search engine optimisation practitioners and "link builders" would have you believe - it is still a factor; and it is useful to understand its primary purpose, in order to develop a Link Building strategy.
The Principle Behind PageRank
Being a student whilst Google was in development, Larry Page was aware that the world of academia had a solid hierarchical basis in the principle of citations. If a research paper on a particular subject contained a reference to a previously-written paper, the paper that was referenced is seen to have been given a "vote" by the research paper.
e.g. this document about Search Engine Optimisation features on page 26 a reference to Larry Page and Sergey Brin's research paper on the anatomy of a search engine.
This is the same as saying this document features a citation for the original paper by Larry Page and Sergey Brin.
Thus the original paper gains a "vote" for having been referenced.