What do you feel when you see that your hair stylist haircut has not-that-good-looking? Or imagine a tailor, wearing a mismatch. You may not feel secure enough in their hands, thinking: " How can these specialists can take care of my hair / clothes if he can not take proper care of his own" Yes, we judge by appearances, yes, the appearance is the type of card. And the same rule works for businesses as well.
While browsing the website of the company that you are considering as a potential provider, you are trying to understand whether it is a professional and reliable or not. And now imagine their website is of lower quality, free template-based. You can find out web design & development company in New Jersey via online resources.
Perhaps, it is not a sign of reliable quality of service of the company, but bad aftertaste is guaranteed anyways. And in terms of a business owner you may not want your potential clients to have this aftertaste!
At this point it is easier to understand the real meaning of a website of the company and its role in creating the first impression of the company (as nowadays people usually search for any kind of information online and the corporate website might be even more important than the "real-life" company's office).