This small positioning revolution is known as "Mobilegeddon" and frames a clear idea: Websites have to be optimized to be viewed from smartphones.
There are many important pages that will be affected. The official website of the European Union, Versace or some Microsoft subpages do not meet several of the "mobile-friendly" requirements and Google is not going to have any kind of regard for them.
This new measure will affect searches via smartphone. However, this is much worse than many may believe given that half of searches are performed from mobile devices, so the consequences can be dire.
They are going to be so strict that it is likely that some websites, which currently occupy the first positions, will move to the second or third page, with all that that entails.