Today people are no longer accessing websites on a computer, but on the go. That means that mobile-friendly sites are a must if you want to get more site visitors. Furthermore, when your website is ranked on Google and the other search engines this is a major focal point that search engines look for. If your website isn't mobile-friendly your ranking will really drop.
Take a look at your stats on your website. They are broken down by the way a person finds your site. You'll see on there that you'll have a lot of visitors from mobile search engine apps. I see on my website that each day around 250 people will visit my site from an Android app. If my website wasn't user-friendly or even mobile-friendly, I'd lose a lot of site visitors each day. The more people who visit your site the higher your rankings are. Google will start to display your content on the home page for people to find it easier. I have noticed that over 75& of my content is displayed now on the first page of Google and other search engines. The articles that people visit most often are always displayed on the home or first page of all major search engines.
Today most website building program have already included a responsive or mobile-friendly design in the program so you don't need to worry about this any longer. All you basically need to do is create your site and the programs will adjust the site to display on mobile devices. All you basically need to worry about is the length of your articles and how much a person needs to scroll down to read them.
I don't think you have too much to worry about today if you are building a new website. However, if you have an existing site online, you should check this site and see if it is mobile-friendly and if it isn't try and upgrade your program or make the necessary changes to your blog or website.