Google related links is a tool that helps webmasters to display related links on the website. This also helps visitors in viewing the most related content as per their choice and also increases page views.
The related links gadget shows the most related pages from your site. This gadget can be embedded in a page and this helps users to reach other related pages easily. Also it shows related searches which are restricted to the site.
Related links was always just a Google Webs Experiment and invitation only service. Not all users can use this related links, as you need to send an Email and request for invitation to use it.
But here comes the bad news. After experimenting with this feature on Google Labs for 1.5 years, Google has decided to shutdown this experiment on July 25th. So webmasters who are using Google Related Links are advised to remove it before July 25th.
Check out the official announcement from here.