Adapting for mobile devices gives your users the best experience. Google reports on its blog that 61% of visitors leave a website it if is not mobile ready and deems responsive web design to be best practice.
The main thing is that you deliver the same content via mobile as you do via desktop. Making sure your content is available to users however and wherever they access your site. It needs to load quickly too, these visitors are on the move and need information immediately.
With Responsive Design we target our website designs at device types and screen sizes. It's a bit like pouring liquid into a glass, adapting to fit the container.