Responsive design is a way of building a website so it automatically reshapes itself to fit whatever screen it is opened on, looking right on a phone, a tablet, and a laptop from a single site rather than a separate mobile version. The text reflows, images resize, and menus rearrange on their own, so a visitor never has to pinch and zoom to read you.
For a small business, this is simply where your customers are. Most people will meet your website on a phone, held in one hand, often on the move. If the site was designed for a desktop and merely shrunk down, they are squinting at tiny text and mis-tapping buttons, and many will leave. A site that is genuinely mobile-friendly reads and works cleanly at that size, which keeps people around long enough to become customers.
Responsive design also means you maintain one site, not two. An edit you make shows up correctly everywhere, so nothing drifts out of sync between a desktop version and a mobile one.
I build every site responsive from the start and check it on a real phone, not just a resized browser window, because a layout is only truly done when it holds up in the hand of the person you are trying to reach.