Google has, ever since its inception, indexed sites (how google looks at a site and decides when to make it appear for users when they type in certain searches) from the perspective of the desktop version/view of a website. However, often the same website can have very different looking websites for both desktop views of the site and mobile views of the site.
This is a problem because a user on a mobile device could search for something in particular which would bring up a website as the number one search result as it answers the user's search criteria, however on the mobile version of the site, the particular item the user on mobile was searching for might not be on the mobile version of that site, but was on the desktop version of the site which can leave the user confused as to where this particular item they were searching for is.
To solve this ever growing problem because of the growing number of mobile users on Google compared to desktop users, Google has started experiments with using mobile versions of websites to index sites rather than desktop versions and Google eventually hopes to primary use the mobile version of a site's content to rank pages from a site. However, Google has stated that they will still index sites for desktop versions but will have mobile versions take priority in the search rankings, aiming to create a positive experience for desktop and mobile users.
How will this effect you? Well, as long as the content of the mobile version of your site is relatively similar or the same, then this change will just be a quality of life change for you and your users and will be nothing to worry about. However, if your site on mobile and desktop are drastically different in terms of content then your users may experience strange search results when attempting to search for content that is/is not on your desktop version of your site. A good idea to stay ahead of the curve is to make this change to your site now if your mobile and desktop versions of your site are different and attempt to make them similar in terms of content, not appearance, to avoid user confusion.