How we view the web changes constantly. Almost on a weekly basis a new tablet or smartphone arrives on the market with a new screen size. If you have a website that's even a few years old, your mobile customers will view it as it's designed to be displayed in a browser on a desktop PC. That can make your website difficult to use and frustrating for the user. People using smartphones are accustomed to apps that are easy to use, with well thought out interfaces.
Your website should work the same way.
Over 50% of American adults access the web with a mobile device. That's 50% of your customers. The goal of your website may be many things, product sales, communication, information, but when it comes down to it, your website is how your customers interact with you and your product or service. If you make it difficult for them, they will go somewhere else.
Enter Responsive Web Design. A modern responsive website is device agnostic, it doesn't care what device is being used to view it, it simply adapts to show information to the viewer in the most usable way possible.
Viewing the example image above you can see a standard website compared to a responsive design as viewed on a mobile device. Right out of the gate, the standard site is not engaging. It requires work to even make it readable. Navigating it is a chore. Pinching and zooming isn't fun. If you have visited a standard website on a smartphone or other small screen device recently you'll be familiar with what you have to go through just to make it work.
A responsive website solves these problems. There is no need to manage and maintain a separate mobile site, everything is in one place. Everything works, everywhere. Everything is accessible, to everyone.