A responsive website is one set of pages that adapts to the screen it is shown on. On a desktop you might see three columns side by side; on a phone the same content stacks into one column with bigger buttons.
It replaced the old approach of building a separate mobile website at a different address. Today it is simply the standard way websites are built.
Responsive does not automatically mean good on mobile. A site can technically fit a phone screen but still have tiny text, fiddly menus or a phone number buried at the bottom.
Many of your customers will find you on a phone, often while dealing with the problem they need you for. If your site is awkward to use on a small screen, they will not squint and persevere; they will go back to Google and call the next result.