Mobile Google Search shows a "more results" button for some users as the company is currently testing the new method for wading through search results with a select number of people. Google's Danny Sullivan, who confirmed on Twitter earlier that Google is testing the new button, states that it has already been testing the button for a little while and that it rolled the new interface tweak out to more users recently. Sullivan also mentions that this will be a change that will only be coming to mobile at this time.
To be clear, Sullivan doesn't explicitly state that the more results button is never going to come to the desktop interface, but when asked whether or not it would be available on desktop too, the response given was "only on mobile," with no follow-up statement of whether or not that means for good. All that aside, the new more results button replaces the buttons for moving to the next page when you have opened up Google on mobile and searched for something. What this does is get rid of loading a separate page on a mobile browser and instead swaps it out for an infinite scroll effect, as hitting the more results button will simply load additional results below the ending of the others.
This should speed things up when sifting heavily through all the results that one can find after inputting a search query, and that's likely part of the reason for the implementation. Without having to load new pages, users will also have all the results on one single, continuously scrollable page, which should also make it a lot easier to go through all the results that pop up. Though Google is testing this new button with more people now, it's unclear how long it will be before it rolls out to all users.