What is pagerank?
PageRank is a ranking system that previously was the foundation of the infamous search engine, Google. When search engines were first developed, they ranked all websites equally and would return results based only on the content and meta tags the pages contained. At the time, however, the PageRank system would revolutionize search engine rankings by including one key factor: a site's authority.
If you would like to see what PageRank your site has or other sites have, install Google's Toolbar. Google has made a small green bar that starts at 0 page rank (a blank bar) all the way up to 10 (a full green bar, which is 100% authoritative). It should be noted that the PageRank shown in the toolbar is an estimate released by Google, and it is only updated every 3 months or so.
When PageRank first came out, only Google was using the technology, but as other search engines have seen how much it improved Google's accuracy, nearly every search engine has added the PageRank system in to be at least part of their algorithm. In the past, while many of the search engines were still working on adding PageRank to their search algorithm, some couldn't wait to make their own and instead signed deals with Google to have them power their results (Yahoo did this for quite some time).
When Google was in its childhood, PageRank was the single most important factor for ranking well. However, as soon as the SEO community caught on to this, there was a great deal of people who found ways to artificially boost their clients' PageRank. Those sites became more authoritative than Google thought they should be. Since then, Google and other search engines have constantly refined how important PageRank is, and its importance has definitely declined through the years.
Now we've come to the part where you actually have to do work! It's tough, but getting a high PageRank for your site should definitely be part of your longterm SEO strategy.
Although not nearly as important as it used to be, PageRank can still be the deciding factor that bumps your site to the top of the search engines. Not only that, but it is also a good indicator of which sites you should spend your most time trying to get links from. Sites with a PageRank 0 are either being punished by Google, or just have an authority of zero, nada, zilch, bupkis, and generally not worth your time.