A responsive design responds to different display sizes by changing the size and layout depending on the device.
The main benefit is that mobile users will receive essentially the same experience of your website as your desktop visitors.
Responsive web design is becoming gradually more popular and many large companies have started to take this approach. Near the end of 2012 Microsoft released a redesign of their commercial website.
Read more at http://www.bugraptors.com/why-responsive-website.