What's the deal with Google PageRank?

Google is my homepage, so every time I open my browser I see that www.google.com, a site with 19 words and a data field, has a PageRank of 10. So what's the deal with PageRank?Do high PageRank sites show up first when you do a search? No. In fact, if you do a search on Google for “search engines”, www.google.com doesn't show up at all. Do the same search on Yahoo and www.google.com shows up in spot number 2, behind www.yahoo.com of course. If Google doesn't manually interfere with their algorithm, and their homepage is a search engine with a PageRank of 10, why does their site not show at all in the search results?This is what Google has to say about PageRank: "PageRank relies on the uniquely democratic nature of the web by using its vast link structure as an indicator of an individual page's value."In essence, Google interprets a link from page A to page B as a vote, by page A, for page B. But, Google looks at more than the sheer volume of votes, or links a page receives; it also analyzes the page that casts the vote. Votes cast by pages that are themselves "important" weigh more heavily and help to make other pages "important". That's great information, right? Unfortunately, I couldn't find that information on Google's site. Instead, I found it on Wikipedia, which is only a PR 7 site. Google itself, on the other hand, gets a PR 10. When searching for Google's own PageRank, wouldn't you expect it to be easier to find information from Google, a PR 10 site, rather than Wikipedia at a lowly PR7?For a while, my conclusion was that the whole PR thing is a scam and that Google is the only PR 10 site. I was wrong. The United States Federal Government's homepage, www.usa.gov, is also a PR 10. The US Senate (www.senate.gov) is a PR 9 as is the Library of Congress (www.loc.gov/index.html) and fellow search engine, Yahoo (www.yahoo.com). The US House of Representatives (www.house.gov), the US Supreme Court (www.supremecourt.gov) and all three branches of the military (www.airforce.com, www.army.mil and www.navy.mil) are all only PR 8s. However, if you're looking for information on any of these organizations, I recommend slumming it with PR 7 Wikipedia.