Mobile search results on Google now routinely show logos (or more accurately, ‘favicons’) next to results. There have been reports recently of the size of these being enlarged, so it’s more important than ever that we all have our favicons set up correctly. You can find out how to set up a favicon here, and if you just want to check how your site’s favicon looks, try this tool here.
One item to note is that in the article above, Google now says not to provide a 16×16 pixel favicon. Once upon a time, this was the only one we were supposed to provide, so it may be worth checking that you’ve got larger sizes and then remove the 16×16 one and references to it.