Your website is the hub of your online business; it is the virtual representation of your company whether your company exists physically or not. When you are doing business online, people cannot see what you physically look like as they could if they were dealing with an offline company. Hence, people do judge you by your covers. This is where a good design comes in.
Imagine if you are running an offline company. Would you allow your salespersons to be dressed in shabby or casual clothes when they are dealing with your customers? By making your staff dress professionally, you are telling your customers that you do care about quality. This works simply because first impressions matter.
Similarly, the same case is with your website. If your website is put together shabbily and looks like a 5 minute "quick fix", you are literally shouting to your visitors that you are not professional and you do not care for quality.
On the opposite, if you have a totally professional looking website layout, you are giving your visitors the perception that you have given meticulous attention to every detail and you care about professionalism. You are organized, focused and you really mean business.
On the other hand, you should also have anything related to your company well designed. From business cards to letterheads to promotional brochures, every little bit matters. This is because as you grow your business, these items become the face of your business. Once again, think of the "salesperson dressed shabbily" analogy, and you will get my point.