Responsive design is an approach to web page creation that makes use of flexible layouts, flexible images. The goal of responsive design is to build web pages that detect the visitor's screen size and orientation and change the layout accordingly*.
GOOGLE WILL BOOST YOUR RANKINGS IF YOU ARE RESPONSIVE
As of April 21, 2015, Google has now included responsive design as part of the algorithm they use to determine where a website is indexed.
FLEXIBILITY & USABILITY
Responsive web design sites allow the content moves freely across all screen resolutions and all devices. Both the grids and the images are fluid. Content is allowed to fill an allotted space and retain its appearance. Responsive web design's fluidity achieves the same result with website content on any size screen.
No scrolling or resizing is needed for any visitor to access your website from their favorite device. The content and images will automatically resize and fit to your screens device. It makes viewing and reading your website easy for viewing on any device, from smartphone to large computer screen.
ABILITY TO BE FOUND ON MOBILE SEARCHES
If your website is not Reponsive, Google will not include you on any searches on a mobile device. You could lose more than 60% of your traffic to your website due to your website not being displayed on mobile searches. From Google: This change will affect mobile searches in all languages worldwide and will have a significant impact in Google Search results.
If your website is not Responsive, you are missing out on a lot of opportunities.