Mobile devices, whether phones or tablets are the norm these days. They are replacing desktops. Given the trend of this technology we need to make sure all web sites "respond" appropriately to these these devices. The screens are a lot smaller than our desktop screens.
Responsive design is not only about adjustable screen resolutions, changing layouts, and automatically resizable images, but rather about a whole new way of thinking about design.
You have 1 web site that accommodates all devices. Having a responsive design increases your search engine ranking.