For example, instead of URLs like www.google.com/about/company/history, you'll see something like this: Google > about > company > history.
Google added support for schema.org structured data for websites, so webmasters can include the site's name and the URL structure as breadcrumbs. You can include multiple site names, but they have to be unique and closely related to the domain name.
Breadcrumbs are already used in desktop SERPs. When they were released, you could click each link to navigate the site's hierarchy, but this feature is no longer available. Google also shows the site's name next to the URL and you can click it to find more information about the site.
Mobile SERPs will add a similar feature and the most important change is that Google will replace the domain name with the site's name. Regular users don't understand web addresses and that's why they use search engines to navigate to sites they visit often like Facebook or Amazon.
Mobile breadcrumbs will gradually roll out worldwide, but site names will only be displayed in the US. I assume that Google will use domain names outside the US, at least for now.
In my opinion, the war against URLs is a bad idea. More and more browser partially hide URLs, Google replaces search results URLs with breadcrumbs and even tests removing them. URLs may be meaningless for many people, but they're unique and they give some information about the site's identity. It's hard to come up with unique site names, especially when you consider that there are many companies, products and sites that have the same name.