"Mobilegeddon" refers to tech giant Google's mobile-friendly ranking algorithm.  It is also known as Mobocalypse, Mopocalypse, or Mobilepocalyse. It is supposed to launch on April 21, 2016.
This algorithm will significantly affect the tech company's mobile search engine ranking parameters. More specifically, it will affect how websites are ranked when it comes to mobile devices.  The change will also affect mobile search results in all languages. Those that meet Google's mobile standards will rank higher in the search results; webmasters can test the mobile-friendliness of their site with a free online testing tool from the company.
It is already slowly being launched. Before that happened, many webmaster feared some significant losses of traffic, so they rushed to make their websites more mobile-friendly.  However, the slow launch of the algorithm has so far proved to not be as groundbreaking as was originally thought.
While there have been definite losses to some sites that had not optimized their content for multiple devices, it has not caused catastrophic losses to many websites like the infamous update Panda. Some major websites have lost their high rankings, while some other sites that were optimized for mobile devices prior to the rollout were rewarded with higher rankings. 
Google seems to be promoting more mobile optimization for those users who access websites on mobile devices. While nothing that major has happened yet, it is believed that this algorithm will continue having more major updates in the future.