Just Before one month ago Google had boost up there mobile friendly algorithm, now Google has started issue for new warnings to the site owners.
As a Website owner if you are seeing this message then its time to update your website algorithm to the mobile friendly website. This message is directly shown to the mobile search result but be noticed that this message will only show to the website owner not to all the search result.
Lets take an example of the Website of Jennifer Slegg she has an old site which is not mobile friendly, she saw this message in there SERP snippet and reported that “Your page is not mobile-friendly” this is hyperlink with Google help page about Mobile friendly.
Here is a snippet or screen shot for the Jenn sees website :
John Mueller of Google confirmed that this is an experiment they are trying out to see if it helps boost mobile-friendliness here is John Mueller Tweets.
@jenstar At the moment it's just those, but I think it's a really neat experiment. Which others should we add?
— John Mueller (@JohnMu) 7 April 2016