Google have recently added a “mobile-friendly” label to their mobile search results (The search results a user will see if Google thinks the user is on a mobile device) and created some tests to help them decide if a given site is mobile friendly or not.
If your site is quite old it will almost certainly need a redesign to pass these new tests.
The test attempts to check if the site design/content display on a smaller screen in a way that is still easy to read and navigate. This is commonly done by coding the design in a way that adapts depending on the screen size and is known as a responsive design.
You can test your site here.