If your site can't be easily viewed on a smartphone, then your design has fallen behind. For awhile, we had to rely on what was esssentially either a very poor interface for the client or a site that looked nothing like the original design. Maybe it had the same colors, maybe similar images, but it simply wasn't the same. Then came responsive design. Now you can build one website and it simply "responds" to the screen dimensions and/or device.
Why is this important? For starters, more and more people are using smartphones and tablets to search for businesses (when I say more and more, I mean a large majority of people). Sure, there are exceptions, but this is where we are heading. Desktops are on their way out, laptops are still viable, but forward thinking marketers are already referring to them as an outdated technology, which leaves us with tablets and smartphones. Tablets come in all different sizes and, while they don't vary quite as much, so do smartphones. Therefore, your website design needs to take into consideration all of these different sizes. Don't worry, it's not that difficult or complicated.
What does this look like? You'll want to design a site that responds to the various differnent sizes of screens available. This would include multiple sizes for tablets, smartphones as well as including desktops and laptops. A decent developer and/or many site builders these days can handle this task.
What to remember: Don't think of responsive design as make it or break it, but as a tool/asset that can help you to better reach your customer. Whether you're a CEO/Supervisor/Manager/Freelancer, you should be using all the appropriate resources available to you.