Responsive website design is done by optimizing CSS and HTML queries of your website to fit all screen sizes. It adapts the layout to any environment to make it optimal for viewing and navigation across a wide range of devices from PC, tablet to smartphones.
Reasons to go Responsive:
90% of people use multiple screens ranging from smartphone, tablet, PC sequentially to access internet.
61% of visitors bounce to your competitors website if your website is not responsive
"Google recommends webmasters follow the industry best practice of using responsive web design, namely serving the same HTML for all devices and using only CSS media queries to decide the rendering on each device"