With the market of mobile phones nowadays has been rapidly increasing, Mostly users tends to buy mobile phones and do browse on it rather than desktop computers. It may have Pros and Cons but I would likely discuss the Pros only since Im really in favor with this new Web Design technique.
One considerable factor of it is it has been recommended by Google for SEO strategy, since Responsive sites have one URL and also has the same HTML whether what device would that be. Then it will be easier for Google to crawl, index, and organize content. unlike if you build a separate mobile version then Google would have to crawl and index multiple version of the same site.
Another factor why it is very important is the User Interface, whether what kind of device is used, the end users will find it amusing, for example some design looks good on desktop and doesn’t look good on the mobile version and vice versa. So with a great responsive design then end users will tend to visit your site likely more often.