Is the site verification by Google Webmaster Tools improves your page rank? If not, then what's the advantage of this?
Hi Google web master is just a tool. You can check your keyword status and number of visits for the respective keywords. There is no nothing between Google web master verification and PR.
Google Webmaster Tools is an essential (free) toolkit for search engine optimization (SEO). It enables you to see your site as Google sees it, shows you which pages on your site are indexed, helps you identify any problems that may prevent Googlebot from accessing certain pages or properly indexing them, and provides basic statistics including keywords users most frequently enter to access your site and which sites link to yours.
Google ask for site verification because google need to confirm that you own a site before providing certain information about the site.
it's just a confirmation that you own the site - giving you access for additional tools that you may use to check/monitor it
Especially if you want to apply good webmaster, you need to do site verification to confirm ownership or being attached or a member of that site
webmasters never increase web traffic its just show that how much traffic you are getting and what is keyword ranking in Google search engine