Responsive Web Design has developed over the past few years to become a device agnostic approach to delivering content to users. Responsive websites are able to adjust their appearance based on screen dimensions, these devices may range from a mobile browser on a smartphone to the tablet screens and all the way up to a HDTV. We can no longer design for a desktop screen with the number of devices and different screen sizes that are available today; and also those that will come tomorrow.
Your website visitors are increasingly viewing your website on a variety of different platforms. It simply makes sense that you would want to ensure that your website looks its absolute best when being displayed on all devices, be it a desktop computer, tablet or smart phone. A recent world-wide study by Google focused on the common trend of "multi-screen buying" and the importance of presenting your website correctly on all screen sizes.
Google will rank you higher. Google knows that close to 50% of their visitors are on mobile devices. It is only natural that these visitors would be expecting to see mobile friendly websites when clicking on search results. Therefore it is in Google's best interest to demote poorly designed mobile websites and in turn increase the ranking of the responsive sites.