Website mentions in the local finder show the search if the search that they used to bring up the local results in Google matches any of the content found on the local business website. Despite the fact that it seems to be live for all, I was not able to replicate the “Their website mentions” notations. But here’s a screen shot by Barry Schwartz:
This feature proves that Google does crawl, as well as surface, local website content, despite the fact that they never actually said that site content is a factor in local rankings. Google has never confirmed that site content is using signals from the site content of local businesses. Its guidelines and tips don’t make any mention of content on the local business website.