For starters instead of a more square-ish search button, the search button has now been updated where it will feature a much rounded design, along with the search bar itself which has been rounded around the edges as well. There have also been some changes made to the search categories, where previously it seemed more attached to the search bar, but now it provides a more floaty design.
However other than that, it seems that for the most part you might not necessarily notice these design changes unless you are actively looking for it or have been made aware about it. Google has been steadily rolling out its Material Design across its various websites and services, so these changes don’t really come as a surprise. These changes should be visible in both the iOS and Android version of Google mobile, so you should see them applied already regardless of what browser you are using.