These six categories represent the primary Ranking Factors -- that is, the things that determine why each website ranks where it does in the search engines. Of course, every search engine has its own secret sauce, but the fundamental underlying principles are very similar.
Page Relevancy: measures the relevancy of a page to the given keyword. A page is considered relevant if it's about the keyword topic, and search engines use a variety of indicators to determine what a page is about, such as presence of the keyword in the page title, headings, images, links, and body content, as well as "topic models" that attempt to figure out what a page is about by mapping relations between words.
Website Relevancy: measures the relevancy of your entire website to the given keyword. Although Website Relevancy is not as essential as some of the other Ranking Factors (just look at all of the Wikipedia pages ranking even though the website is not thematic), it can certainly help. Intuitively, it makes sense that search engines want to prioritize a page about how to change a bike tire that's on a bike shop website, rather than one that's on a bank website. The bike shop website, by having a critical mass of thematically-related content, has to some extent established itself as an expert on this topic, and will get a small boost over a page on an unrelated website.
Page External Relevancy: measures how relevant other people consider a page to be for the given keyword. More specifically, "other people" are primarily other websites, and they indicate to search engines what they think a page is about by using related words in the anchor text of their links to that page. For example, I might link to Stanford and a really awesome SEO tool, and in doing so I'm suggesting to search engines that I think the first page is a University famous for its great Ultimate Frisbee team, and the second is the key to improving your search engine rankings. Pages with a high Page External Relevancy score usually have a large number of quality sites linking to their page using anchor text that is similar to the keyword.
Website External Relevancy: measures how relevant other people consider a website to be for the given keyword. Website External Relevancy is like Page External Relevancy, but for the entire website. In other words, we're looking at links going to your entire website, and trying to determine if people link to your site using words that are similar to the target keyword. Like Website Relevancy, Website External Relevancy is not as important as its page-level counterpart, and should be considered more of a boost rather than a must-have.
Page Strength: measures how important and authoritative the page is considered to be. The most important measure of the importance of a page is the number and quality of links pointing at the page. The more links, and the higher quality the links, the better (high quality links are links from other important, highly-trusted pages). Fortunately, it's not just other websites' votes that count. You also get to tell Google which pages on your site you consider to be the most important. You do this by linking to a page from many other pages on your website. For example, many websites link back to their home page from every other page on their site. Knowingly or not, by doing so they're telling the search engines that they consider the home page to be one of the most important pages on the site. Pages with high Page Strength scores generally have links both from internal pages on the same website and from pages on other quality websites.
Website Strength: measures how important and authoritative a website is considered to be. Website Strength can be one of the most challenging factors to improve, because it primarily depends on getting many high-quality websites to include a link to your website (your home page, or any other page on your website). Many webmasters get into trouble trying so hard to boost their Website Strength that they end up getting low-quality links, which will actually hurt their Website Strength rather than help it. Don't do that! Check out the tips we have for improving your Website Strength in our Action Recommendations instead.