In a nutshell, Google now prioritizes responsive websites which are sites using designs that respond to the size of any given screen. This is different from mobile-friendly sites that can actually be two separate sites that look similar.
How do you know if your website is responsive? Easy - if you're on a computer, just change the size of your browser window to a smaller sized window. If the website adjusts with the browser, then it's responding to the new size. If it just crops out the site and the website doesn't change to the new size, then you have a non-responsive website.
Your website ranking could drop - especially if your competitors' websites are responsive and yours isn't. I tell all my clients that if you cannot get found (easily) on Google, you basically don't exist. If I type in your name and city or business name, you should appear on Page 1. And everyone's page one is different now (that's a separate blog post).
Still interested in learning more? Here's a great article on Search Engine Land for you.
Is this article making your head explode? Then you should definitely call me!!! Especially if it's during normal business hours - lol. Have a great day!