In February 2015 Google posted an article on their Webmaster Central blog entitled "Finding more mobile-friendly search results". The article describes how Google will adapt its search algorithms to find more relevant information for mobile-friendly sites. In fact Google will be expanding its use of mobile-friendliness as a ranking signal for mobile searches.
What is Responsive Web Design?
Simply put it's a web design approach that allows your website to re-size and re-shape to provide an optimal viewing experience for your customer. This means your website will render perfectly no matter the device a person uses. This also means you do not have to design and create a separate website for each device you want your site to work on.