One thing became clear when 2010 came and went: mobile phones are here to stay. And stay they have. Not only that, but they've overtaken desktops in many areas of the web, too. More and more apps and services are aimed specifically at mobile users, with no (or weaker) desktop releases. In at least one month of 2016, Google reported more searches from mobiles than from desktops.
Google also claims that responsive design is one of the most important things a website can have. "Responsive design" is when the same content you see on a desktop scales to fit a mobile phone, providing an identical experience on the same pages to mobile users.
This is experience is considered desirable by many users: losing access to some of the website's content because it has a separate mobile web portal is a sometimes onerous experience. It also creates a little more overhead for the web design team of any given website, requiring them to effectively manage two separate versions of the same website.
And that's also why Google recommends it: because Google indexes mobile and desktop "websites" separately, responsive web design improves your SEO rankings by ensuring that all traffic goes to the same website. And with solid responsive design, a website's customers will not just notice, but appreciate the difference.