Responsive web design is a new trend nowadays and its a approach that suggests the design and development should respond to the user’s behavior & environment based on screen size, platform and orientation.
As a quick example off the top of my head, see Luke Edwards's Website. Mainly watch the menu items when you resize your browser window. As arti18 said, it's got nothing to do with SEO - it only affects how the website is displayed on different screen sizes (think smartphones and tablets).
However, responsive design can be used in parallel with SEO to bring more visitors to your site - with your website looking good on more devices, you have a wider audience.
It would be ridiculous to build a site that does not optimize for browsers size and orientation as two thirds of the market is phone or tablet, and once you find a framework or system that works for you it’s not that difficult to implement this type of extra functionality.
You should also include QUALITY SEO techniques in all your work so adjustments can be made to increase ROI in the future.
I have also made websites that are apps (web apps) that can be launched form android and Apple so it makes sense to me to build in this way.
I have left a link to some of my work here to show what can be achieved.
Responsive Web Design is a web design approach aimed to provide users an optimal user experience across wide range of devices.
Website with non-responsive web design means a separate url and html for each version requiring Google to crawl and index multiple versions of the same site. Unlike responsive websites who has the same url regardless of the device used, which makes it easier for google to crawl and index data.
How is Responsive Web Design beneficial for SEO?
When you have a mobile site that differs to your regular site, you'll frustrate returning visitors who are looking for the same thing that they found on your desktop version. In that case, your bounce rate will rise and your rankings will drop.
Responsive web design allows your visitors to see the same content on both desktop and mobile devices, therefore meeting users expectation and lessening bounce rate.
Mobile Search Ranking
According to Google, it "will rank websites with mobile versions higher in mobile searches" and "recommends responsive web design". Therefore, websites with RWD will rank too in mobile search as a site designed specifically for mobile.
Stronger backlink Profile
In responsive web designed websites, you will have the backlinks of your original site. And, as a mobile usage rises and webmasters start linking mobile sites, your back links from both mobile and desktop will make a stronger backlink profile.
Responsive websites provide continuity between different viewing contexts, remaining completely agnostic to the type of device used and the size of the screen it has.
Formore clearification kindly visit http://www.copyblogger.com/mobile-responsive-seo/