Responsive design is the current best practice technique for creating a site that is optimized not only for viewing on a desktop or laptop computer but also on tablets and smartphones.
While a traditionally designed website will be fully viewable and usable on mobile devices, it often involves a lot of pinching and zooming to view all content. The layout of a responsive website adapts based on the screensize of the device being used to view the site, reorganising content to provide the optimum experience whether the site is viewed on a desktop, laptop, tablet or smartphone.
The benefit to site visitors is they get to view the website in the most optimal way for their device.
Both Google and Bing use mobile-friendliness as a ranking signal and highlight mobile-friendly sites in their search results.