Today morning I am searching for dental treatment gum disease for my treatment. I try one search in Google and I see the different result. Search result show with title link and also inside description link. I not talking about sitelink. title link you have description of website. that website is .gov domain. I think is trusted website for Google that why I see that link in my search result see the below image
Yes It will help to improve your page visibility in your website and Google get more high priority of that link
No it is not because its a gov site, I have seen such links in description for other general sites also.