For a long time, in the early phases of mobile, it was enough if your website displayed okay but required the user to zoom in, for instance, fill out a form or read longer text. In Apirl 2015 though, Google changed the conversation about mobile, making it clear to all that it was time for companies that derived traffic from mobile to take the stet of being mobile-friendly, not just display on mobile device without breaking. I wrote about that effort from Google and what it meant here.
So if you have a website or need to put one up soon, do you really need to care and what does mobile-friendly mean?
Do you need to care? The answer is probably yes. At this point, pretty much everyone who generates website traffic gets at least a reasonable part of their traffic from mobile. Some more and some less but even those that are not very mobile-centric are still probably getting enough traffic to matter. We wrote about mobile traffic here.
The next question is what does mobile-friendly mean? For this, there is a list of things that are required. Not every item is required to be considered mobile-friendly but the more you have the better your site will display and perform.
OPTIONAL BUT IMPORTANT FOR THE USER EXPEREINCE:
Is your site mobile friendly? You can test it here: https://www.google.com/webmasters/tools/mobile-friendly/