According to Yahoo, "Yahoo! Web Rank" is a measure of how popular a web page is based on the number of links pointing at it.
When you enable the Web Rank button on the Yahoo! Companion Toolbar, the URLs you visit will be sent to Yahoo! in order to get its Web Rank (from 1 to 10). The info sent about the URL is anonymous and DOES NOT include your Yahoo! ID or any personally identifiable information.
According to me, It is not like Google Pagerank in any way, Though Yahoo says it takes links into count I feel it is not the case, They mostly check the popularity of the site from people using their toolbar and use that data to assign a webrank to it, This is another good feature of yahoo to get into a direct competition with the Big G, Google is our words,
You can turn off Web Rank at any time from the Toolbar Settings menu (pencil icon). When disabled, URLs are no longer sent to Yahoo!.
SO how does Web rank feature work?
The Yahoo! Web Rank feature of the Yahoo! toolbar works by collecting anonymous URL data about the page you are visiting. This anonymous URL data is sent to the Yahoo! Companion servers, and a Yahoo! Web Rank value( which yahoo knows already) is returned to the Yahoo! Companion Toolbar as one measurement of the link popularity of the Web page or URL you are visiting.
You will see a small icon on your Yahoo! Companion Toolbar displaying the Web Rank value (on a scale of 1 to 10) of the site you are currently visiting. Web rank is measured by the link popularity of the web page, Mostly i feel Yahoo gives a lot of weight to sites in Dmoz and yahoo directory, According to them Dmoz is an expert hub and links from it is credited a lot, We have a site with about 500 backlinks in Yahoo showing a Yahoo webrank of 0, ANother sites has only 20 links but one link is from an important category in Dmoz directory that site has a Yahoo web rank of 4 which is really surprising,
Also the big bug I saw in the web rank feature of Yahoo is the webrank of Google, Google has one of the most powerful backlink on the web but Yahoo says Google's Webrank was 0, Which is a Bug in their system, But later it was rectified and now it shows a webrank 10 for yahoo which is a good sign, May be Future is good for Yahoo's Webrank feature but right now it is not too much of an SEO attraction,
How do I install the Yahoo! Web Rank feature?
First you have to download the Yahoo companion toolbar from Yahoo, When that toolbar is downloaded you have to install the Yahoo! Companion Toolbar, then you will have the option of enabling the Web Rank feature. If you would like to use it, choose the "Install WITH Web Rank" button on the configuration page and the Yahoo! Web Rank feature will be enabled during the installation of the toolbar.
Important feature of Yahoo webrank is helps in alerting the Yahoo! Search crawler to the existence of a particular Web site or Web page, and direct a crawler to visit that Web site or Web page for inclusion in Yahoo! Search if it is not already in the Yahoo! Search index. This is an important feature and helps you in possible inclusion in the yahoo index, Yahoo crawler is the 2nd most active crawler on the web and I feel you will have a good faith that Yahoo slurp is triggered by this webrank feature.