Responsive design lets your website self-adjust itself to fit the device it is being viewed on. There is no need to pinch and push the tiny text of a website when being viewed on a smart phone. It allows for a seamless experience for viewers.
Why responsive design? Fifty percent of all local searches are done on a mobile device. Additionally, a responsive website will rank higher in mobile Google searches and will provide a professional and easy to view display of your website on any device.