As was first reported in January by Search Engine Land, and has more recently been covered by mainstream publications such as Forbes, Google will be using Mobile-Friendliness as an important ranking factor. The official start-date for this change is April 21st of this year.
If your website has Google Webmaster Tools installed, and your site has mobile issues, the person who set up this account should have already received a warning. Whether or not you received such a warning, you should use this free Mobile-Friendly Test tool that Google has created. 
If you pass this test, then you are good to go. Your site will qualify for the mobile friendly label, and will not be penalized in search results.
What to Do if You Don’t Pass the Test
First of all, don’t panic. Next, consult with the company that built your website, and/or other web developers to determine your best path forward. Depending on how your website was built, it may be able to be retrofitted. If not, you’ll have some decisions to make about whether you simply want to stick with your current design, recreated in a mobile friendly manner, or if it is time for a full redesign of your site. Remember, while this April deadline is important, your main objective with a project of this scope should be to make sure your website is suited to your needs for the next several years or more.
