Hyperlinks were the main method of building the Internet and connecting sites through HTML, allowing people and bots to move around and find what they needed. They were like any other citations, methods of getting additional information by going somewhere else.
Contrary to popular belief, Al Gore didn't invent the hyperlink. The term itself was first used in the 1960s, before most of you were born.
In 1998 there was the first on-paper mention of PageRank, just before Larry Page and Sergei Brin actually founded Google. The theory behind PageRank became part of the basis of the Google algorithm, and continues to be so today.
To greatly simplify the concept, PageRank is a popularity contest wherein the pages with the most support (via inbound links) behind them should be viewed as the most important ones. You could increase a page's importance simply by building as many links as possible to it.
As anyone who deals with SEO knows though, it's a lot trickier than that.
Not All Links Are of Equal Importance
A link from the homepage of a powerful site like the BBC will be of a higher quality than a link from the links page of your high school's blog.
If a competitor that ranked above you in the SERPs had 100 more links than you, you couldn't just go grab 101 links and rank above him. Some links are simply more valuable than others, particularly links from authoritative sites (like respected news sites) and links from .edu and .gov domains.
There's a point that gets lost a lot, one that makes it obvious that actual PageRank and visible PageRank are two very different things.
The PageRank that we can see represented in the bar, a number, from a PageRank checker, etc., is updated infrequently and isn't the actual PageRank that Google assigns to your site. The actual PageRank calculation, if shown here, would make all of our heads spin. Let's just say that it's a lot more complicated than a number from 0 to 10.